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

Oct 18, 2015

$x = {\log}_{7} \frac{2}{2}$.

#### 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

${\log}_{7} \left({7}^{2 x}\right) = {\log}_{7} \left(2\right)$.

For what we have just observed, it becomes

$2 x = {\log}_{7} \left(2\right) \setminus \implies x = {\log}_{7} \frac{2}{2}$.