Hello guys welcome back to this channel! In the previous video! We spoke about the loss of indices and in this video we have some examples? We are going to try our hands on now? We are going to solve these four questions and then we are asked to find the values of x!
Now, let’s start off with the first example, so, for example, one we have 32 exponent x equals 0? 25 now to find the value of x. We need to make sure that we have common bases or we have the same basis. Then we can compare their exponent and find the value of x! Now we can simplify this to have 32 exponents x equals one over four now one over four is the same as zero point two five!
Now this is equal to 1 over 2 exponent 2. . Now 32 is equal to 2 exponent 5. . So we have 2 exponents 5 all exponents x, which is equal to two exponents negative two now in indices, there is a property such that whenever you have one over a exponent n, where a is not equal to 0, you can express that as a exponent negative n. So if you have 1 over 2 exponent 2, then it’s equal to 2 exponents negative 2. So that is what we have here now we can multiply the exponent! So we have two exponents: 5x equals two exponents negative two! Now, because we have common bases, then we can compare their exponents, so we have five x equals negative two. Now, let’s divide both sides of the equation by five and then we have x to be equal to negative two over five. So this is the value of x! Now, let’s solve the second example.
For the second example, we have three exponents: five x plus 3 equals 81 exponents x, plus 3, and we are going to find the value of x. Now 81 is equal to 3 times 3 times 3 times 3, which is equal to 3 exponents 4. . So we have 3 exponents, 5x plus 3 equals three exponents for exponents x plus three. Now we can multiply four and then x, plus three, so that’s going to be 3 exponents, 5, x, plus 3 equals 3 exponents 4 into brackets x, plus 3. . Now, because the bases are the same, let’s compare their exponents, so we are going to have five x plus three equals four into brackets. We have x plus three now 4 times x is 4x and then 4 times! 3 is 12. . Now, let’s transpose 4x to the left hand side.
So we have 5x, minus 4x equals we have 12, and then we transpose positive 3 to the right hand side so that it becomes negative! Three now five x, minus four x is x and then we have x is equal to twelve. Minus three is equal to nine, so the value of x is equal to nine.
Let’s move on to the third example: for example: three we have one over eight all exponents, 4x minus 9 equals 64 exponents, 3x, plus one now, according to indices, one over eight is equal to one over eight exponent, one which is equal to eight exponents negative one. So we can simplify one over eight as eight exponents negative one exponent.
Four x minus nine, which is equal to now. 64 is equal to 8 squared. So we have 8 squared exponents, 3x plus 1. .
Now, let’s multiply the exponent across.
So we have eight exponents negative one into bracket? Four x minus nine equals eight exponents two into brackets three x, plus one? So because we have common bases, then we are going to compare the exponents, so that is negative. One into brackets four x minus 9 equals 2 into bracket, 3x plus 1. , now negative 1 times. 4 is negative 4, so you have negative 4x and then negative one times negative.
Nine is plus nine. Now two times three x is six x and then two times one is equal to two. Now, let’s transpose six x to the left-hand side, so we have negative 4x minus 6x equals we have 2, and then we have negative 9. . So you have negative 10x equals negative 7, and then we divide both sides of the equation by negative 10, and then we have x to be equal to 7 over 10!
So this is the value of x for question number three! Now, let’s solve the last example so question four: we have three times: 9 exponent, 1 plus x, equals 27 exponent negative x. Now we can simplify this as three exponents, one times three exponent, two, that is for the nine and then we have exponent one plus x now three times three times three is twenty seven, so we have three exponent three times negative x. Now, let’s simplify theta, so we are going to have three exponents one times we are going to multiply two and then one plus x, so that is going to be three exponent two into brackets 1 plus x, that is equal to 3 exponents negative 3x. Now in indices.
Whenever i want to multiply common bases, then you want to add their exponents. So a exponent m times. A exponent n is equal to a exponent m plus n! So that is what we are going to apply here. So we are going to have three exponents, one plus two into brackets one plus x, and that is equal to three exponents negative three x. Now, let’s compare their exponents, so we have 1, plus 2 into brackets. 1 plus x equals negative 3x. Now, let’s multiply across, we have 2 times 1, which is 2 and then 2 times x, which is 2x equal to negative 3x! Now, let’s transpose 2x to the right hand side, so we are going to have 1 plus 2 is 3, and that is equal to negative 3x minus 2x and that is equal to negative 5x? So we divide both sides of the equation by negative 5, and then we have x to be equal to negative three over five.
So that is the end of the video thanks for watching like and subscribe for more interesting videos, bye.