Answer
$\log_2{\left(\frac{1}{8}\right)}=-3$
Work Step by Step
The given expression is equivalent to:
\begin{align*}
&=\log_2{\left(\frac{1}{2^3}\right)}\\\\
&=\log_2{\left(2^{-3}\right)}\\\\
\end{align*}
Using the rule $\log_a{a^b}=b$, then
$\log_2{\left(2^{-3}\right)}=-3$
Thus, $\log_2{\left(\frac{1}{8}\right)}=-3$.