Answer
$x=\frac{1}{8}$
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, $log_{x}2=-\frac{1}{3}$ is equivalent to $x^{-\frac{1}{3}}=2$.
$x^{-\frac{1}{3}}=\frac{1}{x^{\frac{1}{3}}}=\frac{1}{\sqrt[3] x}=2$
For $\frac{1}{\sqrt[3] x}=2$, multiply both sides by $\sqrt[3] x$.
$2\sqrt[3] x=1$
Divide both sides by 2.
$\sqrt[3] x=\frac{1}{2}$
$x=\frac{1}{8}$, because $(\frac{1}{2})^{3}=\frac{1}{8}$
