Answer
$x=5$
Work Step by Step
If $b\gt0$ and $b\ne1$, then $y=log_{b}x$ means $x=b^{y}$ for every $x\gt0$ and every real number $y$.
Therefore, $log_{x}\frac{1}{125}=-3$ is equivalent to $x^{-3}=\frac{1}{125}$.
We know that $x=5$, because $5^{-3}=\frac{1}{5^{3}}=\frac{1}{5\times5\times5}=\frac{1}{125}$.
