Jon P. answered • 09/12/15

Knowledgeable Math, Science, SAT, ACT tutor - Harvard honors grad

Any time you need to solve an equation with the unknown in the exponent, you are likely to need to use logarithms. That gets the unknown out of the exponent.

First take the log of both sides. You can use any base for the logarithm, so let's use base 10:

5

^{x}=2log (5

^{x}) = log 2Use the rule for exponents:

x log 5 = log 2

Divide both sides by log 5

x = log 2 / log 5

That's the exact answer.