Answer
$-2$
Work Step by Step
RECALL:
$y=a^b \longleftrightarrow \log_a{y}=b$
Let $y=\log_2{\left(\frac{1}{4}\right)}$.
Using the definition above gives:
\begin{align*}
2^y&=\frac{1}{4}\\\\
2^y&=\frac{1}{2^2}\\\\
2^y&=2^{-2}
\end{align*}
Use the rule $a^m=b^n \longrightarrow m=n$ to obtain:
$2^y=2^{-2}\longrightarrow y=-2$
Thus, $y=\log_2{\left(\frac{1}{4}\right)}=-2$.
