Answer
$2$
Work Step by Step
RECALL:
$y=a^b \longleftrightarrow \log_a{y}=b$
Let $y=\log_7{49}$.
Using the definition above gives:
\begin{align*}
7^y&=49\\
7^y&=7^2
\end{align*}
Use the rule $a^m=b^n \longrightarrow m=n$ to obtain:
$7^y=7^2\longrightarrow y=2$
Thus, $y=\log_7{49}=2$.