#### Answer

$\frac{1}{5}$

#### Work Step by Step

Rewrite the equation in exponent format using the definition of logarithm.
$7^x=\sqrt[5]{7}$
Rewrite $\sqrt[5]{7}$ and $7^{\frac{1}{5}}$ to get two bases that are the same.
$7^x=7^\frac{1}{5}$
If $a^b=a^c$, then $b=c$. Therefore, $x=\frac{1}{5}$.
$x=\frac{1}{5}$