Answer
$x=5$
Work Step by Step
$\log_{x}\dfrac{1}{125}=-3$
Rewrite in exponential form:
$x^{-3}=\dfrac{1}{125}$
Rewrite $x^{-3}$ as $\dfrac{1}{x^{3}}$:
$\dfrac{1}{x^{3}}=\dfrac{1}{125}$
If $\dfrac{1}{x^{3}}=\dfrac{1}{125}$, then $x^{3}=125$
$x^{3}=125$
Take the cubic root of both sides of the equation:
$\sqrt[3]{x^{3}}=\sqrt[3]{125}$
$x=5$
