Question

The Method of Common Bases works because exponential functions are one-to-one, i.e. if the outputs are the same, then the inputs must also be the same. This is what allows us to say that if 2^x = 2^y, then x must be equal to y. But it doesn't always work out so easily. If x² = 5², can we say that x must be 5? Could it be anything else? Why does this not work out as easily as the exponential case?

a. Yes, x must be 5. The reasoning is the same as with exponential functions.
b. No, x could be anything else, and it's not as straightforward because squaring is different from exponentiation.

Answer 1

The Method of Common Bases does not work as easily with x² = 5² as it does with exponential functions. If x² = 5², x could be either 5 or -5.

Step-by-step explanation:

The Method of Common Bases does not work as easily with x² = 5² as it does with exponential functions because squaring is different from exponentiation. This means that if x² = 5², x could be either 5 or -5. Squaring a number always gives a positive result, so we have to consider both the positive and negative square root of 25 in this case.