Answer
$\left\{72\right\}$
Work Step by Step
Since $\log_b y=x$ implies $y=b^x$, the given equation, $
\log_3(x+9)=4
$, implies
\begin{align*}\require{cancel}
x+9&=3^4
\\
x+9&=81
\\
x&=81-9
\\
x&=72
.\end{align*}
Hence, the solution set of the equation $
\log_3(x+9)=4
$ is $
\left\{72\right\}
$.
