Number three, if 2 to the power x is equal to 15 and 15 to the power y is equal to 32, then what is the product of x and y equal to? Let's take a closer look at the equations we are given. We have 2 to the power x is equal to 15. We also know that 15 to the power y is equal to 32, so somehow we have to introduce a power of y, and we can do that by raising both sides to the power y. Then this is equivalent to saying that 2 to the power x times y, which is the number we're looking for, is equal to 15 to the power y, which we know already is 32. So we have the equation so far, 2 to the power x times y is 32, which is equal to 2 to the power 5. And so the only possible number here that we can use in the exponent when the bases are equal is 5 for the product of x and y. We can also take logarithm space 2 of both sides and obtain the same answer. So, the answer is 5a.

exponentiation

logarithms

algebra

equations

mathematics