Question

How do you solve `7^(2x)=2`?

Answer 1

`x=log_7(2)/2`.

Explanation:

We need to isolate the variable. Since the logarithm is the inverse function of the power, which means that `log_a a^x = x`, if we take the logarithm base `7` of both members we get

`log_7 (7^{2x}) = log_7(2)`.

For what we have just observed, it becomes

`2x=log_7(2) \implies x=log_7(2)/2`.