Answer
$x=-3$
Work Step by Step
First, we let
$\log_{2}{\frac{1}{8}} = x$
RECALL:
$\log_b{y} =x \longrightarrow b^x=y$
Use the rule above, where $y=\frac{1}{8}$ and $b=2$, to obtain:
$2^x=\frac{1}{8}$
Write $\frac{1}{8}$ as $ 2^{-3}$ to obtain:
$2^x=2^{-3}$
Use the rule "If $a^x=a^y$, then $x=y$" to obtain:
$x=-3$
