Answer
$x=-3$
Work Step by Step
We know that if $b\gt0$ and $b\ne1$, then $y=log_{b}x$ is equivalent to $x=b^{y}$ (where $x\gt0$ and $y$ is a real number).
Therefore, $log_{2}\frac{1}{8}=x$ is equivalent to $2^{x}=\frac{1}{8}$.
Therefore, $x=-3$, because $2^{-3}=\frac{1}{2^{3}}=\frac{1}{8}$.