# INDICES – SHS 2 ( CORE /GENERAL MATHS)

Today, our topic is indices. Now, if you have a to the power n now we call this.

This is the exponent and this we call it the base and if you have e to the power n, this means that you have a times e times e times. It means that this e is multiplying itself, that is n times or all the years in that this is what n factious the most when this e n times? So, if you have a to the power 4 infinity of e times e times e times e, how many times four times, if you have e to the power, let’s see three, this e times e times e plus 3 times, and then also, if you have 2 to the power 5, that is 2 times 2 times 2 times 2 times, 2, that is 5 times 1 2 3 4 5.

And if you have 1 over 3 all the plastics, it will be multiplying this 6 times. So you are 1 over 3 times 1 over 3 times 1 over 3 times, 1 divided by times 1 over 3 point 2, 3, 4 5 the last one times 1 over 3! There are a lot of we use double guide us to be able to simplify questions like this and then the first rule?

Let’s consider the first rule the first receipt. If you have a to the power m times a to the power and the first rule is saying that when the bases are the same, they are multiplied!

You have to add the exponents here, darby into the pot and plus n another fashion!

Now, let’s consider the following example: not the first one. We have white power three times y to the power 5. Now the loss is that when the bees are the same in your multiplying up the exponent, so the base is yy!

So you add the exponents so here let me why three plus five- and this is y to the power 8. Now, let’s see the second one, you have r to the power three times r to the power 15 times to the power 7! When the bases are the same, your mods probably are the exponents. Here we have our 3 plus 15, plus 7 and currently 3 plus 15, that is 18 plus, and that is 25 to the power 25. Now, let’s see the turtle you’re 4x squared right to the plant 3 times today, x y to the party, so you have numerals in front of it? So there are 4 times 3 that is 4 in 3, then x, squared times x, plus this time! This then times y q, times y squared now this the visa regime! So this just to the power 1 so 4 times, 3 that is 12 times x. This would be 2 plus 1, because x with any power that is the price 1, so 2 plus 1 times y, we have 3 plus 3, so don’t be 12 x to the power 3 y to the power 5 2 plus 1, that is 3, 3 plus 2. That is 5. Now, let’s see the fourth one we have 2a squared b times 3 a square b cannot write 2 times 3, so we have 2 times 3 a square times.

Another e squared out this and this and there’ll be times v 2 times 3.

This is 6, then ya, be a 2 + 2 b 1 + 1, not 2 + 2, that is 4! So we have 6 a square and then b to the power 2, because 2 + 2 did you give us 4 and then 1 + 1. This is equal to 2?

Now, let’s see the fifth one, we have 6 p to the power 3 times, 2 p square times 4 p to the power 4 times, 2 p all to the power 5. Unless the numerous beneath start teams, we have 6 – 4 to 6 times 2 times 4 times, 2 p square times, p to the power 4 times p to the power 5, not 6 times to 12 12 times 4, that is 40 to 50 times 2, that is 96 or fe 2, plus 4, plus 5. We are multiplying. These are the same. So we add the exponents? So here we have 96 p 2, + 4, that’s 6 6 + 5, and this is 11! Now, let’s see the roots, what is the root to see the roots? we saying that anytime, you are dividing and the bases are the same.

You subtract? So if you have n to the power m all over a to the power n, now we are dividing, so you see that e, -, n or it can be put- and this way that is a to the power m divided by e to the power m! So this is a minus m, so anytime that we are dividing and then the bases are the same?

We subtract the exponents now, let’s consider the following example: the first on e to the power 5 divided by e to the party, so we have first one a to the power 5 all over e to the party. Now this we are dividing the bases are the same. What do you do? we subtract the exponents, so here we have a to the power 5 minus 2, and this is 5 minus 2. This is a to the power 3. Now, let’s see the second one p to the power 7 all over p to the party we are dividing. So here we subtract the x when you have p to the power 7 minus 2, and this is p to the power 5. Now, let’s see the third one, you have 8 p 6, all over 4 p to the power 4 now here or can see for greens of 1/4 going to eat. That is 2 time? So we have 2 p 6 minus 4. What is 6 minus 4? that’s what we have you, and this is 2 p 6 minus 4, that is 2. Now, let’s see the fourth question: 18 p to the power 5 all over 3 p to the power negative 2, now trillion safe, 13!

8, another 6 times, 6 p 5! Now this ability to subtract.

We are negative: negative 2, not negative negative bb, positive 3 of 6 p, 5, plus 2, and this is 6 p to the power 7. Now, let’s see 5 18 x, squared y to the power 6 all over 2 x y to the power 2. Now, let’s see to we’re one to great that is 9 eating time. That is 9, so we have 9.

So, let’s see x to the party. My here s 1 so 2, minus 1 y to the power 6 minus 2, but this exists so -, and this will give us 9 x y to the power 6 minus 2 dollars. For now, let’s see question 6. We have x to the power 5 times x to the power 3 all over x to the power 2? Now here, let’s see we are multiplying extras. What do we do? we are? we have x to the power 5 plus 3, all over x to the part.

Why are we adding because visiting your mods being art, so this is? we have x to the power 8 all over x to the power 2 5 plus 3, that is 8, and this is that is x 8 minus 2, and this is x to the past x, because 2 minus 8, x minus 2! This is giving us 6. Let’s see question on box 724? We are one for green 32. This would be that is 8 times we have 8 ko 9 minus 3. Then you have armed 4 minus 1, and this is 8 q na minus 3.

This is 6 and then out to the path 3 4 minus 1- that is 3 now, let’s see, example form what seemed fine? Definitely. The first verse is that i 5-piece keep times 2 p negative 5 honor to be to the power 4. Now that’s what we have over here.

What do we know- and this is telling us when what, when the bees are the same- we add the exponents so clearly 5 times 2, we can see if i don’t, which is 10, but then p. We have p to the path, 3 plus negative 5, all over p to the powerful and is the same as t. That is the octane here, 3 minus 5, that is giving us negative 2 all over p to the power 4? This can go on top, so we have 10 p negative 2 minus 4. Why are subtracting peter? the panic is repeated a powerful because we are dividing. We subtract the exponent, so we have 10 p- 6 policy, the ii/3 to the past 7 times 3 to the power negative 2 all over 3? Now, what is it telling us arrest elena’s that william? what? when visiting, we are the exponent so 20 here we of tetrapods 7, plus negative 2, all over 3 to the power 1. Now we have 3 7 minus 2, that is 5, and then we have 3 to the power 1. Now this would be 3 5, minus 1, y 5 minus 1. In that we are dividing. Be that same so you subtract the exponent?

So we have 3 to the power 4 honestly to the powerful. It is about 3 times 3 times 3 times 3, and this is just 81 now, let’s see question omatsu that is 30 over x y squared, divided by 6x, squared all over x, squared y. Now we have to note that if you have a over b divided by c over d, this division to change multiplication and you reciprocate the second time you reciprocate the second time in the same way, let’s say we: this would be not tightly for x y squared times x square y, all over 6x squared y division. We change what multiplication reciprocate! The second time can i see! Can you see the xs cancel e naught x, squared six wins of one system in 20? that is five times now! Let’s see we are this two. This is one, so they are, that is 5y, but because it’s 2 this is 1? We have 1 minus t because we are dividing all over x. This is the same as 5 negative 1 all over x? We can rewrite this, as that is 5 over x y. Now why? let’s the property we say is that if you have a to the point negative and is the same as 1 all over e n, so if you have two telefónica decimals wonderful, so if you have x to the point, negative is the same as 1 over x so y to the point. Negative 1 can come down and we can have this unless sufficient whistle the division into multiplication? So you have x times between two y squared all the tweets. One explains: malassezia rings are one nice summon holy month.

2020 i was fine? Not what do you have planned? a look at the meters, 5 x 1 square. The denominator becomes, that is x square y, with you already expressed before a why now, because we are dividing the bees as in expects subtraction? So here we have 5, x, 1, minus 2, 1 to the power 2 minus 3, and this is 5 x, negative, 1, 1 negative 1. Now what do you have? currently? this can be written as 5 over an x y! As i said this, you know if the problem may be even be the same as 1 over e, so there is a property but i used to like him! Now, let’s see this too, so this division here to change to multiplication, we have 9 eq b, squared all over 2 c to the power 4 times it becomes 4, pcs, all 3, a squared p to the power 4. But here let’s see today contains 9 and then the two forces we want to uniform?

That is two times \$9. 00? Three now for police, really listen to the numerator. Now, yes into the past three into the pot one senior into the country, plus one your piece will see to the party oliver, the less nothing the defects would eat to the pond to be to the powerful and in ufc also to the pond, and even us play into the pop of the stripper before being to the want to see to the party all about aids before to be to the prophecy to the powerful what we do below.

But if your what’s my visa is, what do you miss of public school, so yeah this yesterday ii? this is the first of four minus two and then the signal will be minus 4 and then i don’t see 2 -, 4 8 to the party. That’s beautiful, and this can be written as three is all about b squared c squared because we argued the property is equality which is a fallacy through trade. Now, if you have novice 8 the part and all the bottom here we see that you multiply the immigrants we have seen n times n.

Now, let’s see so if you have simplify the following [music], the first ability to the party station and to the pond six on the vaccine and this, if you’re not serving the car the services of into the pond one watson out to the pond. For now, let’s see how you to simplify this applying the rules we have t to the policy after the path is vdc. We have to multiply the exponents with us two times three and it is t to the power 6. Now, let’s see the second one over to the coccyx, this will be n to the 6, and this is 10 to the power 3 know: let’s see what do you do? we multiply the experts. We have some internet quality. What are some into the public soon have some! This is tonight. Well, i, see you mean fall if you have it be all to the part in this is equal to. This is a to the path and b to the power n. Now this is negotiations that that it be odds the part in it.

We multiplied. That is n time that is and focus and then solving alice n factors, and this is the same as when eating eat. We think that we need this one and then also eat it. Now this one is 10 times we have beat the party, and this feels ten times b to the party, and so then we are saying that they be all to the pocket is equal to a and b, not a slippers example. We have simplified palace, the first one we have 2x all to the pontoon and from the roof. This is just to write x? Squared, it is just 4x plus 2. Squared is what paul does in the alternate parking in business. It can be now, let’s see the second one.

We have 2 5 all to the party so yeah they say me that is 2 squared times with 5-pole spread, not discrete multiplying it with fun? So this is 4 5 5, squared it’s fun the 4 times 5 this is sweet? Let us see the third one we have 3 piece will be c c to the portal to the quadrant! Now applying the rule, we have traded to the par 3 a to the 1/2 times, 3 c to the power 2 times 3, including at rhythms that this is giving us between seven eight f-16 c to the power six not mess in there full pressure? We know that [music] to the party to the bathroom here for 2 to 16 or younger to the eat, 27 no 2 times 2 that is x to the policies y minus 3 times 2, the greatest 9 is 16 times in science. We are 16 times x to the 8th, there’s another texas so 6 by 6, because we are 16 x, and this is y 2 plus 1. Let’s see this example simplify that is 302 pocket square divided by e to the power 340b to the phone. That’s what we have! We know that if you have it be on to the part and it’s into the pot and b to the pilot, so you have 20 about the party. This is this all of us [music]. This is justification. [music] three-one-seven go into 14, plus 2 times 2 times that didn’t give us 18 less serious. Each department each department, so this would condemn me to the lannister.

Then you can be to the power to beat upon by the school, and this is equal to negative b, negative 1?

So 2 minus 1 is positive, positive 1 now! well, thanks! i can rewrite this? I know that if you have equality, it is 1.

Therefore, all about, let’s see 2 to the power 2, but this, but now, when you gonna do up the exponent of 2 negative 4, 6 plus 3 is 9 [music] to the negative 4 these artists, in what you do -, but for 13 criticism [music]. This is for deaf i’ve, seen an example: blessing [music], [music], [music], [music] [music] for ^ be able to define it had been pulled up yet so it treats the profit business – for 3 over 4 to the power palace 1024. Now, let’s see one, the third one, the seeker, it’s the part 2 times, 4 to the power n, plus 1, all the time 60, but when we commit all the business, the scene first, crop beans for two eighty-eight deceive us to depart for me and their days. – awesome? Thanks for getting fortitude to the party and all of our – to the party and it continued to to the power i spoke to to the platform using a 16 on this is equality. We have 2 to the power 6 2 to the power 2 plus 4, plus, because when you are multiple disciplines, the business is, you add the exponents now in the cmos due to the oh.

Now, let’s see we are multiplying. So what can we do here? now we can subtract the b dot. C square root button is just two to the past six plus two plus one minus plus two plus four y?

These are the same, so we subtract now this one is for. Did you give us? the 6 plus 2 is 8 minus 4, so this will give us 4! So this will cancel this. Nobody happy? What is it 2 to the power 4? this is 16 and what is 16 16 is this, but as consider the fluid properties under illnesses, cockpit, we have a nonzero number to the power! 0 is 1, so if we have 2 to the power 1 by 3, 1 utama, our total answer is 1 and then also, if you have a to the power negative indecisiveness one uma, the \$50 speed to the public is an option, a reduction from this. If you have e, who have be all to the power negative n now, that’s the same as b over d and then the negative.

Who are we? what i supposed to just reciprocate and really risk it’s the negative who are we- and this is the c- must be to the pub and e to the party. Now, let’s see, if you have b will be all the one negative and other people maybe deep end, and then we know that if you have knowledge, you have e to the power negative, and this is amos 1, comma negative positive in this can be written as a times.

1 -, not me now. This is, he must want to eat the parking and istanbul on totally how we, the porosity, then so literacy must be the part in all over into the parking this he must be in on this? Now fractional chemists so give me off cake to fall one, what instead the cmos. This can be written in this form and then also, if you have a to the power m over n, this can be written up.

That is e, and this we can write this as n times. 1 in my pen did the seamless into the front end, and this can be written in duck into the end, the stevenson. This is amorphous all to the end of to the file. Now, let’s see you this example, she give a like the flu in the first one that is 16-bit. One of us, edit, the scene fast 61 about to the spare me this is one was the same. A spirit of cysteine and root of 16 is the same as for all or if you have succeeded for one or two now, because you have one what we here system i can change this thing as fall to the park because wanted a part of the civil system, so i wanted to turn to? This will cancel this, and this will give me for this is one ring things i mean today to the bathroom.

We have three now, let’s see [music] to the power one, two three now from yeah below it, we all to the pub.

You know that ap all the point, this is e and the end.

This implies that we are [music] reference. Now you can take this also to tray to the pathway, extra comma y to the park, because because we are negative, because this is negative, even if you are participating, because what do you value all to depart? positive entry refers to our sermon, prince simon oliver eats at the dedication whose we are [music]! Now, let’s see five six now this is what we have away, because it’s negative! What i was supposed to do? basically, three or 6000 gone, but about five of us x, the negative you are we need now! This is five over six insert into the past.

Six should give us the sixty four to three past releases before the process we are and to the power. This is 32. Now, let’s this example, the sermon was 64. Multiple negative to attract this is a possible question, so 64 negative.

Now this is negative because of the negative r.

We are disappointed? What is in the bracket, so this will be cvt. Who are we, and this is the c- must be c.

This is to our flesh. We have to change this to a lot of the positive changes tunable to the partner. All to the pathway is a senior 64 today to the powerfully?

C must be served to now.

Let the same as party department times 3 1, 3 2, the party [music] [music]. Let’s see try to two ounces, hopefully to the battery the you must words and claim from here the number to the power 3 2006 to the factory in give us that we have 6 to the par 3 thanks to mr.

Johnson? Is there are six to the parts this is giving us 10 to 6. Now, let’s see the 1/16 all the parties, for this is two or four? What kelly no idea, the sixteen to all the powerful click. The policy must equal 3 over 4, and this the same now, this will cancel that the lessee, the numerator. We have no be 2 to the power 4 times 3 to the party of the parking. This is in p. M.

This! What we do, but this will cancel this all over here. We are turning to the power 3 to 2 times 2, to the power 3 e to the power 2 times 3, which is 6 all about 3 cleavage will be that is 8 over 3 17 to the power 6? Now, let’s see one, we have 49 to the power other words plus 125 to the 1/3 off to the power to novice. We ought to simply find a parking space? So, yes serving to the party times one of our two blasts. This one refers to the foramen ovale! This is 5 to the par 3 21, what they all to the part with this recursively this responsibility, so they are supplied bracket space bombers. What a 7 plus 5 so plus 5 is closed? We have 12 to the party what is close to the party.

This is 12 times 12, and this is 144. It means the to simplify the filling me up for about three to four five x to the power minus 27, who, when you can typically see, we can see them coming all the bases to see so yeah.

Let’s see, we have 1 to the power 5. Now this we can expect disaster into the pot goes 3 to the party, the cmos? Now we are writing it in this, because we are a to the part and see that little cos e is a multiplies! The a that is what yeah now you’re super into the party.

Everything is cmos only 1 e n, so this can be expressed as greater unity, 5 x, 2, x, 3, 1, 3, plus 1? Now the bees are seeing what was what we have their school in three, because it is much business password class to go in venice today, [music] yeah now and + – – -, my feeling that we serve you get used to be a story about a swimsuit three? Now, let’s see the second there’s, a possibility run about 64 all over 1 to 5, and this is 3 now bracket face butler, so leather, the bucket face – invited by now the sling is what i supposed to be recipe so that the negative moves away and this to a friend because he was ready. He retreated and about to depart from give us 125 in a matter to tell give us 64, [music] [music] [music], although to the party- and this is an unfortunate part- 2 verse, 16 motivation which into multiplications we have two times six in anova that is 25 now in america, no matter what 2016 is 32 1 times 25, we have 25 times, 25 go into 32, that is 1 times, and what we have here! This will be submitted all over 25 when i see this form, not in the public / 15 about to depart negative. Sir. Now because of the negative 1 million resolutions, we have 25 times 2 to the power 4 divided! This would be does to 15 a little far positive, 2 community of ill, what the ultra park and is a and beaten glen, and because it is one move on to is a seamless first departure oliver to to the party. Now this can be to the park form the same of 16 available or all [music] [music] watch me now, which of the properties are supposed to use.

Look at the par negative n is 1 over n. So this is just one spirit of primus will be.

We have 75 hadn’t become changed!

Paladin english means 475 one what this disease not drove to the park? well, now? what can we see this constant? is you one time this? this will be 25, but i was 23 times please giving us 30 35 this one’s easy, no [music]. This is because of the negative as soon as progressive cookies. The negative is supposed to do is to who are we so right here? this will be dallas negative 27. This will be 2 over 3, nobody had negative a negative, and then we have 2 or 3. So sometimes the partner will trade to the path? Green and give us to go a friend so now my sphere of nicotine, let’s see that in r1 we can let their one of us ligety today the positive 1/3 of the party, but this is consoling us, so this will give us plus negative negative 3 all to the party. This will be nice to negative life in disappearance. Now, let’s see the second which are going to to simplify, followed by x y all to the power. Sorry, these bees are to see they’re divided to subtract? This is quite on 1!

This is 5, so let’s calculate this one, this one. So this beatable me twice: n minus 1, and this is x to the to the party and then this one. So it’s what i’ve written here? What? finally two dots? all this so larry? what do we do? we take a we multiply by the second term?

That is the second bracket we take v to the party [music] before into three miss p 1, p, 2, 3, plus b 4, 2 & 3. Now we are multiplying these accessory attic space.

We are get p, 1 plus 2, by this time. This we have e 1, dot square plus 1 over terrain, and we are b:g understood who are thrilled that the solution we have t 1 will be 4 over 3 [music].

This time this we have e1 with bella, be too much too much this time, this bb cream.

None of this is we are one of our today, plus 2 or 3, and this case you know whatever you give us once we have eat whenever this no nasty place. This one is just the same as a 1 of a 3 plus 1 or 3 the usual sorry, not here i see we have minus e to the c must be, and then this one does too, of a plus for rutland is a six. Hoorah trapeze fee to the party.

Now, let’s see what can we see now this, and that are the same, so this will cancel that no, this one and no one to simplify it is some an exponential equation.

We have two cases, let’s consider other case from the first is, if you have b to the power alice n equal to b, to the power a here, because the exponents are the same received by the the business closes. You see me to be and indicates to the kids to see that if the bases are the same, then you quit dance when in sweden into the power and important into the power, and here the blazes are essentially be.

We equate the exponents we see. L is important and let’s consider examples, analyst cases now.

Let’s see this example soft x, the following the first one. We have three departments important line when welcoming you, because if the base is the same for into the vortex, not trip to the park to the same islamic god that these artists embodied in queen, victoria texas equal to two now, let’s see the second one we have, we are multiple delivers, have you’re multiplying. So these are seen without a spoon to possible. Well, here the biggest axis, when you equate the exponents poor servant for now, let’s see question tonight, we have 5 x to be equal to 5 to the 1 negative 1, because we are dividing the beats at the scene? What did we so product? we have 5 x minus 9 to 5 negative 1, not for me what we do!

These are the same? So what did we get that we have as well? it’s not equal to negative 1, mrs! To beta x 2 equal to negative 1, plus 9 and x is equal to. That is negative one. Last time this is giving us these things solve the following equation: the first one x to the power 5 equal to negative, so the first one we have x to the power 5 equal to 2. Now here we have the part we find here? You can also pick the bug to be fine, so here you have x to the power 5, and this now be 2 to the power 5 is 32 and because the exponents are, the c is implied the see, no sure if we have others into the part and equal to b to the party we are seeing that e is equal to pc’s. What exponent policy? now, let’s see the second of x -1 equal to 64, not here clara, can see, expose, went to the pasture? It now here to be convict that parcel to be the same asterix? We have x minus 1. The default rate here it can be as far as fall to the contrary is also giving us 64 and called the expletive, see me with the beasts equal to 4. So this community of x, plus 1 and now, let’s see, question number 3, yeah selected apart x equal to 1, not here, meaning the base is the same student in quit. Desperate, we observe into the pot i see a video serving the public, so listen to the plaza is one if it’s is fall to the park x and it’s one and can also change it for deposit. So it is good. The pieces are the same again with it as well.

See next important. So let us see the fourth one? We have two x plus three all to the five one, five three miami to make the exponent the c! So here we are 2x, plus 3, and here five to the part, three is giving us one in france, with larry amin, 2x plus 3! What fact why an explanation equates the basis for vanya to x can be put 5 minus 3 to x 5. Minus 3 is given as true and clearly here can find x by 24 side by 2, so – thanks a lot x to be equal to one and also if we are blessing 1 over 4 y -1 equal to 1, they want to find y look at it here, 1 over 4. He has to be continuous to it. Wonderful, because if you have a to the pastor, is 1 so because it emits 104 here to achieve to one before a wonderful for my mother’s only was one two or for the deposit, because the basics liquid expletive 1-1, because a y equal to 1 so for x in the funding e to the power x equals 1 over 2. So the first one, a tech support one over to first, let’s make all the bases the same 8 define this the sin of 2 to the company 1 under small? What about you? it can be a personal student electron negative because we would, if the quad negative. That is what one who ha in claim the mitsuba seems. We quit exponent 3 x equal to negative 1. Therefore, x is negative 4, let’s the second one, one in a thoroughly to the part, that’s equal to root of 3. He a clearly commit the business in one of our free and written as 3 to the 4 negative 1 speak world today to the part under what – screams of the cmas wonderful to know this!

This will be probably operated upon negative things because biggest one times indicated they wanted to little upon one to watson. What we do we can impede this we are exporting to these are the same, will be the exponents we have x infinity 1 over 2 receivership 3, you know fall to the power 2 x -1 equal to we talked to when working in we commit the base is the same here to to the parts means the cmos for, and this is two to the power one for the base. Alice’s! Would it be credit screen, -, 2, x, – 1, because 1 / 2 less expunge as far as minus 2 d equal to 1 to r to turn it from the air seems to to moderate side by 2 we get x minus 4. It won’t work because 2 times 1 what will the cinemas 1? this has good days!

We got it x equal to 1, plus 4 x, equal to 5 xs! Now that’s question number 4! We have 16 – x, equal to 1, plus 16, no living on this side.

We can check this out so that the basis to be the sames we have 16 to the part equal to 16 to the part negative 1 the basis to be the bbc. Are you know it’s the public? it n is one of our year. 20 bits are essentially equally explosion, -, that’s a possibility for access, but we divide each side by 2 as soon as possible, once print x? We have to be all the babies the same so here? There’s not responsibility here under the 16 can cases in us 2 to the power of 2 to the power 1 minus x, and because we are dividing by 0 so far, 3 or 3 to the power [music]. Let’s see, let’s see the first one. We have rate to the power 2 x minus 1 equals 9 robotics.

It will connect the pc to see three to the power two audio lickety-split to the park to explore the spoon in court today there are negative? Two is plenty. The big success really modified, explaining nexus 1 busan bye. For now, let’s see the second question: we have e to the power x plus 1 equal to 1, to 1 for typically b to c.

You can see this between the department getting suited to the party, so we have 2 to the power 3 x plus 1 equals 1 1 2 to the power 2 is the same as 2 to the power 3 x plus 1 equal to 2 to the power negative 2.

The base that excessive index mu, 1 equal to negative 2? You can expect a good day today, x equal to negative 2 minus 3 is giving us negative 5 1 5 x. So this is negative 5 over 3? Let us see person number 3. We have 4 to the power 2 x minus 1, what 16 to the public 1x! Clearly this is for x now applying a formula e and two e and two counselors. We are formed -, excellent [music], all the days to to ultimately give us 64 2 to the power 6 receiver since before he has 2 to the power all visually 2 to the power 1 minus n, equal to 2 to the quality or the earth to end now, as we have a basis at the scene.

What do you do? we are experts just to 6 and plus 1, all over 2 for 1 that is n equal to 2 to the power 4 and 2 times 2, giving us 4 head. No, the pits are the same! We are, they might want it to be some trucks tree up to 6, 10, plus 1 minus palace form 1, minus n, equal to 2 to the power 4 in the beta ac equal to cb equates the exponent so glad we have 6 and plus 1 minus 4, 1 minus n equal to 4, and we have 6 +, 144 and multiple? Unless bengali can see, let me guess the top side. We have 6 n, plus 4 and when it is fought in equality, we have negative 1, plus 4! Now this process we have 6 in equal to 3. We won’t fund any very cybersex one two!

This was very possible!

You have local to so this one [music] pinsir to it from here? You want to find it in this end if you run across what is you because this is one? what way we keep [music] the weapons sites, so this repulsive history- and this one is eight today can be 8 plus 1 n is like want to find anyone you do.

We divide both side by 3 n is equal to 3. Now, let’s see, question 2 9 to the part 2 x, equals 1 to a 3 is 7 thanks. First, let’s make all the pieces see this one? We do need a party to answer what about today, please and symmetry to the power 3 x. Now these are the scene by dividing we subtract so from here for x to the power minus 1, 1 minus 1, because, let’s see you value, this one is 3 to the power 1 2 3, 3, x, minus 1 india is not values. We get the points! 12 is allison liquids, the exponent of x equals 3x, plus 1 x equal to 1 x equal to negative 1. Now, let’s see, question number 3 x to the power 5 equal to 1024, to the power 5 to give up spent reading for planning for to the power 5 is the same as 10 to 1024. You gotta explain everything!

We do x times e to the power x equal to 1. What are supposed to make all the btcc to the power because the bigger the pieces to know. Let me hear your multiplying business allison to be unhelpful imported to to the father. Let’s see these are simply click next [music].

What x approach negative 2, so you have to give every side by 4 x axis equals negative 1.

This will be 1?

This way to not here clearly have 4 to the power 2 minus x times, 16 to the power x plus 1 equal to 64, with amic on the pc? Let’s, because a base for we are four times here for the party aseema 16, all to the part 3?

These are the simian! What works we are yet minutes, plus forty-four to the par-3. The business is going to be pretty expensive to run s x, plus 2 plus 1 equal to 3, and this is 2 plus x, plus 2 x, plus 2 equal to 3, 2 plus 2 is giving us 4 negative 2, x, plus x, plus 2 x? This will give us x equal to 3?

What do you do? turn it from here? x is equal to 3, minus 4 and i access negative 1, because it is the same idea.

You can change this into 2 to the power 3.

The bigger baits are the see what i did there. Missy must to 1 minus y plus y minus y, because you’re multiplying these are all this? This awesome country of – to the plaster all over 2 to the power 1 plus to go to the factory -. What these are see. We are dividers what you do you subtract x goes to minus 2, minus 3, 1 beta 2, beta xt, [music] minus 5? Clearly from here, what can we do? we have to expand a limited one by the 3/4 6-9 mark? This time, which is evidence, be honest- this has to be a business becoming the limit? 1 – versus a squad equal to eight, don’t find one bedroom side by eight [music], one plus two plus x equal to e to the negative three x? Bees are the same between experts, 1 plus 2, 1, plus x, equal to negative three x. Now, let’s explain: 1 plus 2 plus 2 x equal to negative 3, x 1/5 x. Now what is the history plus 2 x equal to negative 3x? this must determine discussed, included, 2x +, 3 x equal to negative 3/2, x plus 10 minutes, maybe 305? But let’s see the second line to the power 2 x plus 1 is 1x to break the vortex. What are we supposed to make all the pieces? the c so here this plane to the parts, because the 9 2 equal to 3 to the 4x minus 2, all over 3 to the x! Now as a promise, we are trained when we can expand ability’. They exponent. You know for x, plus 2 system is like that equal to 3 for x when it’s x.

These are seen equate the exponents oakland. What les is funding support x when it’s intimate aspects of your projects plus to know, let’s see your voice, whether it’s let’s bring up the uniform, it’s a small place, plus it wouldn’t eat this. You today, – -, no friendly to architects! We have x? Let me in – -! This is negative? Big! all the babies i see here we gonna be most motorplex! We have 9 – x, is equal to 3x plus 3, so they can lick. The beater seems of the last week! My business will be the exponent 2 + 3 for text 26 equal to x, plus 3. Now this was to convey this was the movie – 4 x 2 – trans people to 3, plus x 3 x equal to my own faith! Ecumenical side by 3 plan by x is equal to 3 plus 3 into 9 three times. Let’s see the fourth one we have 180 1 x 2 equal to please everyone.

Whether states, you have me, call the base to see one when it sticks. Now? We know that if you have a about these diseases, what about ian signal signal signal, so this one is the same as the next big allison? Let’s consider this example that is 8 inch by 2 to the power x plus 1 equal to 2 square root of 2 to the power x? So the first one we have 8 2, x, plus 1 2 to the power x? Now this is states and this each we can check this in 12!

The same b’s are the two wires, so we can change it 8 to 2 to the power 3 times. This will be 2 the same thing x, +, 1, 2, now 2, that is 2 times? This is 2 to the power x to the power 1 over 2? Now what is happening the way because we are multiplying these are the same? We add the exponents so in a nutshell, and get 2 to the power 3 plus x, plus 1 equal to 2 to the power 1 times 2. This would be just x over 2. Now this one will be 2 to the power 3 plus s? We have 4 plus x equal to 2 to the power 1 plus x 2, but because the bases are the same, we have an equal sign. We equate the exponents we have 4, plus x equal to 1, plus x? All over two familiar theme is to matra 2 by 2 plus 2 times 4 2 times x 2 times 1 plus 2 times x over 2.

This will cancel that now we have 8 plus 2x equal to 2 plus x. We group like terms to find x so the actual economy of 2x minus x? This is come here now we are three year. It is going there so that minus 2 minus 8 now 2x minus x. This is x and this is negative. 6 now the first one!

Now, let’s also see the second question! The second question is 2 to the power x square: minus 24 equal to 16, to the power x. Here! What should we do? we have to make the bases the same. So this is to the 16.

Now system can be changed you to to the perform so not is to to the powerful, and it’s going to multiply the x naught beta equals? We equate the exponents, so you have x, squared minus 24 equal to 4x, so that’s also chemistry of x, squared minus 4x, minus 24 equals desire to know my fellow motor again negative 2 in for me, and we get negative 4 that is negative, 6x and positive to negative 6 and positive 4. Now this is what is called access: ecology of x, minus x, plus 4x minus s equals r x minus x.

Minus s is common thanks when the sex is called! Factors are what you are. A x plus 4 equals l, so we have x.

Minus is equal to 0 or x, plus 4 equals 0 x equal to 6 x equal to negative 4. Now, let’s see the third question as well: we have 2 to the power x. Squared minus 5x equals 1 over 64. We have to make the lcm the same. We have 2 to the power x square, minus 5x equality? This is the same as 1 over 2 to the power 6. Now you have 2 to the power x. Squared minus 5 is equal to 2 to the power negative 6. These are civic with the x to the 3 of x square? Minus 5 is equal to negative 6 i get a quadratic equation, so we that is x, squared minus 5x, plus 6 equals y plus a negative crossing becoming positive, not universally motor gets x? When are they get negative, 5 – negative, 2, negative 3. You know x, squared minus 2x, minus 3x, plus 6 equal to 0 this to water scone access commons. We have x minus 2, minus 3 of x minus 2, because their exponents 2 extra lashes come on bring it down. What is left here, x minus 3, equal to 0 tournament records? Are we have x minus 2 equal to 0 or x minus 3 equal to 0? clearly we have x equal to 2 or x equal to positive? Throwing now.

Let’s see this example solve the following: the first one, 16 3, pi n we’ve got the cube root of 2 to the power 2? This is may june, 2018 question number 6 now, does it what am i supposed to the face make all the bg’s the scene you can change this to that? is this okey this? we can change this as 4 to the power 2 n and this cube root is the same mask! What do you do to the purchase two dollars for and only of q, which is 1 over 3 now this can be expressed as 4 to n rotifer to the power 1 over 3. Why the searching to this unity of e m- and this is a and at the end the m multiplied the end from here.

We can equate the exponents we have to and what one was very.

What else is a mystery 3 times 2 3 times, 1 or 3 tests concerned that we have 6 n equals 1 and equal to 6 going to fine, and so we divide both side by 6 2, which is 1 2 by 6. Now, let’s see the second one, we have 1 over 3 to the power x times nine to the par 3 over 300 ma 1 over 2, all over 3 equal to 27 to the power 2 over 3. Now here we can make all the bases the same? Now.

How can you change this? we know a to the power negative end is the same as 1 over l.

So this is a master e to the power negative 1 or x times. This one is 3 to the power 2, and this can be 2 times, 3 6, plus 1 7. We have 7 over to all of our throwing equal to? You can change this to be that a strain to the past 3 and we have a side 2 over 3. Now we know a if you have, that is a and all to the part- and this is e and so much value of 3 to the power negative x times 3 to the parties to consider sue’s. We have 7 all the way 3 equal to this one would be right little bit 3 times, 2 or 3. The tokens are the suit ring to the power to register console-based living the two over there? Now we are multiplies what you do?

We add the exponent, that is, the numerators! We have 3 negative x, plus 7, all over 3 equal to 3 to the power 2. Now this one, we relate to the power negative x, plus rn minus 1, equal to 3 to the power 2. Now we are subtracted because we are dividing business are the same. We can equate the exponents.

We have negative x, plus 7 minus 1 equal to 2. Now this has to go there, but we have negative x, plus 6 equal to 7 minus 1?

We have negative x equal to 2, minus 6, negative x, equal to negative 4 2 minus x, that’s negative 4. We can’t vet, you buy the negatives, we have x to be equal to positive 4. Now, let’s consider question trader the stretch: the pi x plus 3 to the power x plus 1 equal to 36. Now this is no more easy. This is addition now from the rules of indices, which one can we apply here.

We can apply the first move, the first. We see that if you have e to the power m times e to the power n is equal to e m plus n. So it means that this is just the seen as that, so you can break it down like this. We have today to the power x 3 to the power x plus 1. If god says this will start from this, we have 3 to the power x plus 3, to the power x times 3 to the power 1 equal to 36. Now 3 to the project straight device is common, so you can factorize it out, so you have 3 to the power x! What’s left, 1 plus 3 to the power 1 in quality, that is what is 1 plus 3 for your 4 times, 3 to the power x equal to 36! Now this multiplies we can divide through by 4, so we get to by 4.

We have 4 times 3 to the power x all over for 36 all over 4? This is concerned another we have 3 to the power x equal to 94! We are following techniques now times become big. The base is the same, so we have 3 to the power x equal to 3 to the power! These are the silicon equate exponents!

We have x equal to 2. Now, let’s see question number 4, the fourth one sees that you have 2 to the power x plus 2 to the power x minus 1 equal to 48. Now we can apply the phase rule on this, so this is 2 to the power x plus 2, to the power x times 2 to the power negative 1 equals 48.

Now from here, what is common 2 to the power? x is calm, so you can factorize it out. We have 2 to the power x what is left 1, plus 2 to the power negative 1 equal to 48. Now, let’s say mass 2 to the power x. This is 1 plus 1 over 248? What is one plus one was? we can change this as to what which should be 3 over 2. So we have 2 to the power x times 3 over 2 equal to 48. We cannot write you by the lcm, which is 2, so here we have do the same as 2 times 2 to the power x times 3 over 2 equal to 2 times 48!

That’s what cancel that we have 2 to the power x times, 3 equal to 2 times 48? We can write true by trey what is matt rynders! We have 2 to the power x times, 3 1 over 3 equal to 2 times 48, all over 3.

This will be 1. This way 16 this and this recurrence? We have 2 to the power x 2 times 16, which is 32. We can make the basis to say 2 to the power x equal to 2, to the power 5 to the power! 5 will give us 32, and this implies. X is equal to 5 [music]. You create the exponent x equal to five? Now, let’s see this example of small solve the following: 2/3 part: 2 y plus 2 minus 9 interval 2 to the power y equals negative, 2, so thatís what we have here and klan, let’s bring this to here and equal to zero. We can see this can’t be transformed into a quadratic equation, so you have 2 to the power 2 y plus 2 minus 9, into bracket 2 to the power i plus 2, because they’re using the first rule, we can break this one down. We have 2 to the power 2 y times, 2 to the power 2 minus 9 like a 2 to the power i plus 2, because, oh you can see 2 to the power here 2 to the power y here, because also changes 1 to 2 to the power, but it’s continued to fall.

So this implies that is 4 2 to the power y all to the power 2 minus 9, 2 to the power y plus 2 equal to 0. Now, clearly, we have 2 to the power bi at the square, so this in the form of a quadratic equation. So you can see let e be equal to 2 to the power. This implies that we have for a square. So this is a minus 9, a plus 2 equals 0. Now that’s a quadratic equation, which of the second case so 4 times, 2, which is 8 to nose and multiply i get it.

When you add you get negative 9, clearly negative 8 and the negative 1 we have for a square, minus 8, minus a plus 2, because then what is coming here for is community of a minus 2, minus 1 e minus 2 equals earned even still a minus 2 minus 2 for y -1 equal to z? We are more intuitive concerns! We have a mystical alpha, p minus one.

People deserve a 4200 for eight plus one n equal to one google! For now what yeah? we know that we know that that is two to the power.

Y is e, so when e is 2, nothin is the first one. What are we going to get we’ll get 2 to the power i equal to 2? but this is the power 1.

Therefore y is 1 and also when a is 1 over 4, we have 3 to the power y equal to 1 what we can change the basis to be the same. 2 to the power y equals 1 over 2 to the power 2 2 to the power n, constitute to the power negative 2 y equal to negative 2? Now, let’s say this example: question number 2 2 to the power 2 x plus 2 minus 5, divided 2 to the power x plus 1, well 2 to the power x is here! We can also get them to the power x? Also very less apply the first rule over here.

So we have 2 to the power 2 x times, 2 to the power 2, and this butonce onto this minus 5. We have 2 to the power x plus 1, equal to 0 or 2 to the power! 2 is 4, so you are falling here! This can be change to be 2 to the power x or to the power 2, because this can multiply this and we can get this so minus 5. You have 2 to the power x plus 1 equal to 0, to surprise we can let it to be a so! You can say that let 2 to the power x be equal to e. This implies that what we have are 4, a squared minus 5a plus 1 equal to 0 motor for by the constants? We are for generally much vaguer for when you are doing a negative 5. So this is negative, 4 and a negative one. So far, a square minus 4, a minus e plus one equal to zero? What is common for it is common, so you have p minus 1 minus? We have a minus 1 equal to 0 p minus 1 for e minus 1 equals l, so most went to the sequencer. We have y minus 1 equals 0 for y minus 1 equals m equals 104 e.

It was one here is 1 over 4, but what we knew in order 2 to the power x is equal to e! So when e is 1, what do you have? 2 to the power x 2 to the 4 x equal to 1 equal to 1? now here we have to make the bases they seem. This is 2 to the price and yeah. Definitely the base should be 2 so 2 to the power to give us 1/2 to the passivation, because any knowns are no matter. The puzzle is 1, so you have 2 to the power x equal to 2 to the puzzle!

This implies x is equal to 0 and then also when a is 1 or 4.

So we have 2 to the power x, equals 1, 4 4 2 to the power x discontinuous 1 over 2 to the party, and we have 2 to the power x and is the same as 2 to the power negative 2, pi e to the power negative x 1 over and clearly the bees are the same things with the exponents. We have x to be equal to negative 2. Now, let’s see the third one, we have twitter x, plus that it will try to trap a negative x minus 12 equal to so we can see two to the power negative xa? We know that if you have, that is a to the power negative- and this is this- is not 1 over a so let’s apply this over here, so this one, but we have 2 to the power x plus 32, all over 2 to the power x minus 2, all equal t.

So we have 2 to the products to the price?

We can see that led to to the power x the arrival we can choose a you can see light 2 to the power x be equal to e. This implies that a plus 32 over a minus 12 equal to zero lcm is a become a 33.

By h we have a times a plus a times: 32 minus 12 times a equals l!

This will give us a square, but this is 8. This will cancel that plus 32 and it’s two of a equal to 0!

We have a square minus 12y, plus 32 equal to 0-2 no mess? When you multiply you get that stated to any article negative 12. That is. This is clearly negative, 8 negative form, so you have a square minus 4, a minus et plus 32 equal to z. What is common is konzi of a – fall -. It’s a minus 4 equals l in – form a minus 8 because they’re too much when two teaspoons, as we have a minus 4 for 4 – eat because clearly is equal to 4 or is equal to 8. But then what do we know? we know 2 to the power! X is our a?

We know that but 2 to the power x was equal to a so when a is 4, so you have 2 to the power x equal to 4. We have to make the base is the same so 2 to the power x equal to 2 to the power 2, clearly access to about the other ones. That is when is 8, so you have 2 to the power x equal to 8 when the base is here we have to make the base is the same 2 to the power x equal to 2, to the power 4, the 2, to the power 3. To give us 8? we can equate the exponent x is equal to 3? That’s an example under simultaneous equation by error still under indices? Let’s see our such questions are so all this pops question is solve for x and y in the following equations: the first one 2 to the power x plus 4 y equals 1, and at the new york around 2 to the power x, + 8 y equals 1 over phone now, the first one. This is what we have in this! We have to make the bases the same this one we have one so first to make the business a.

We can change this one to 2 to the power 0! So we have 2 to the power x plus 4 y.

Let’s go to 2 to the power z 2 to the power.

0 is 1. Clearly what do we have? x plus 4y equals l. We can see this is equation.

1. Now, let’s see the second equation that is 2 to the power x, plus 8y equals 1 over 4 we can make?

The base is the same here so 2 to the power x, + 8 y, equal 2? This is 1 over 2 to the power positive 2? The bees are on the same here so here we have to apply the other. We see that e to the power negative and is equal to 1 over e, and so here we have 2 to the power x, + 8 y equal to 2 to the power negative 2. Our energy of e to the power negative is the same as 1 1 and for me we can equate the exponents. We have x, + 8 y equal to negative 2.

Let’s call this equation 2. Now that’s exodus exactly! we can use the addition method, so we can say that equation?

2 – equation 1, so x – x is given as l. It’s 1 minus 4.

This is giving us that as 4 y equals non negative – manager, that is negative, 2 won’t find y?

So we can divide both side by 4, so we have 4 y 1/4 equal to negative 2 over 4! This is canceling on that we have 1. + 3 y equals negative 1, but you won’t find x -!

Let’s put, we can see that put y equal to negative 1 over 2 into any of them. We can see into equation 1 what is equation 1, which is this? we have x, + 4 words y negative 1. What in courtesan this way? 1 this way? – 2, x, -, 2, equal to 0 as equal to positive 2? This will go -.

We are going to get that now. Lastly, the second one, if 3 to the power m times 3 to the power n equal to 240, 3 & 3 to the prime divided by today, – the parts when you go to 9, write down two equations connecting m and inherence, which you find the values of m and n.

So the first one this what we have here, actually we can make the biggest that seems. We have 3 to the power m times 3 to the power m. This is the same as 3 to the power 5, because our calculator to check we are multiple visiting.

We are the exponent 3 +, + n, equal to 3 to the power 5. We have 3 to the power m plus n equal to e to the power 5 liquid ecstasy of m plus n equal to 5, and this is, if we see one now, let’s see the second equation, 3 to the power and divided by a to the power 2 and equal to 9! Now, with this, the bases are the same? So what do you do? we here we offer its rate by here!

2 is also a so let’s make this to have a piece of tray today and divided by 3 to the power 2 n, and this is trying to the power 2, which is 9!

Now, let’s see we are dividing and because we are define what the degree subtracted x when we are 3 and minus 2 and equal to 3 to the power 2, which principle did we use built the second resist if you’re dividing these are the same, you subtract the exponent? Clearly we can equate the exponents!

We have m minus 2 and equal to 2 equation.

So now this is equation 1. This is equation, 2. What we can use, either the substitution or against the relation.

Let’s use the substitution method that is equation: 2 minus equation 1, so you can see that equation: 2 minus equal human now m minus m- that is a negative 2n minus this n-dubz negative, try n equal to 2 minus 5. That is negative 3? You won’t find any. We divide both side by negative 3. We have negative 3 and oliver negative 3 equal to negative 3, all over negative 3 and sp protons.

We can say that, put or substitute and equal to 1 into any of them because equals 1. Now we need which one is this ooh and and this one because 5.

5 m, so you have m to be 5! Minus 1 is 4 now the third one, if 9 to the pi x times 3 to the part where equals 1 over 7 to 9 and then 2 triple negative x times 4 to the power negative y, you got one right: did you find the values of x and ok? now from the first one? that is the first equation. We have 9 to the power x times, 3 to the power 2 y equals 1 over 7 to 9. We have to make the bases the c? We can check this to treat the part 3 of x x times 3 to the power 2 i equals 1, not reach the power to give us a win to know that is 3 to the power 6.

Now because we are multiplying, you add the exponents. We have 3 to the power 2 x + 2 i, why we are multiplying equal to 3 to the power.

Negatives is why if you have e to the power negative in the same as 1 1 anything now these are the same. What did you equate the exponents? we have 2x +, 2 y equal to negative 6 twist a factor follow that we can divide by 2. We have x + y equal to negative 3.

Let’s call this equation 1 now the second one we have 2 to the power negative x times, 4 to the power negative y! You got 1 over 8? We have to make all the bases the same, so you have 2 to the power negative x time. This will be 2 to the power negative 2y y. The to multiply the right includes 1 over 2 to the power 3. Now we know e to the power!

Negative n is 1 over n.

We apply it over here, so you have 2 to the power negative x times, 2 negative 2y equal to 2 to the power negative 3 applying the rule over here? Now we are multiple bases, are the same. We add the exponents, so we have 2 to the power negative x minus 2 y equal to 2 to the power negative 3. These are the same. You equate the exponents. We have negative x, minus 2 i equal to negative 3 negative running through you can divide through by the negative theory of x plus 2 i equal to 3, and let’s call this equation?

2 nice equation. 1! This is equation. 1 this equation 2. Clearly we can use elimination method, so you can subtract. So you can see that equation! 2 minus equation, 1 now x minus x is l2 y minus y is y and then 3 minus minus 3. That would be 6, so we have our y to be equal to 6. We can say also see that put y equals 6 into any of the equations that i can get x, let’s say into equation: 2 we have x, +, 2 y 6 equal to 3 2 times! 6 is 12, x plus 12 equals 3, and then here clearly won’t find x rays. Portray minus 12? X is equal to.

That is negative money. Well, that’s the fourth one notice.

This was a past question: listen of the queens 19, if 3 to the power x times 9 to the power equal to 4/3 and 3 to the products divided by 3 to the part where you got 1 over 27, the original, which you find that is x plus y? Now there’s the first equation, so you have to make all the biggest the same.

So you have 3 to the power x find this is 3 to the part y or the 3 to the power 5. Now we apply this rule vitality of e and all to the point you said, ii leave the rule that we use. Now we are mod, spend easily. Since what you do we add the exponents we are throwing x plus 2 y equal to 3 to the power 5 now bases are the same. What you do equate the exponents, yeah x, plus 2 i equal to 5! Let’s call this equation 1 now the second one says that 3 to the power x divided by 3 to the power 2 i’ve got 1 over 27? Now, what can we do here? we can change this thing 7 to 3 to the power 3, so you have 3 to the power x, divided by 3 to the power 2 i 1 over 3 to the power 3, now a to the power negative and is the same as 1 over n. That is e trapani, given this is equal to 1 over n. So you have 3 to the power x, divided by 3 to the power 2 y equal to 3, to 4 negative 3. Now we are dividing here we can subtract the exponent? These are the same, so x minus 2, i equal to 3 to the power negative 3 bases are the same!

We equate the exponents, so we have x. Minus 2 i equals negative 3.

Let’s call this equation: 2 plus reverse equation 1 this equation 1- and this is equation 2! Looking at that, we can add the two equations, so you can say that question one plus equation two know x plus x. This is 2 x, 2 y -2, and that is l and then 5, minus 3 is 2! Clearly we can’t find x? We can write u by 2!

So our x to the cotswolds then also put x equal to 1 into any of them.

Let’s say into equation: 2 now x is false.

We have 1 minus 2 y equal to negative 3 want to find y. So let this go.

– we have minus 2y? We’ve got the negative 3 minus 1 minus 2y called the negative 1/4 + y. We divide both sides by negative 2. Well, so young, why to be equal to two? but the question is you defined x plus y, therefore x plus y? what is x x is 1?

What is y at y tv 2, so 1 plus 2? this is equal to 3? You! .