Answer
$x=5$
Work Step by Step
First, the solutions must satisfy $\left\{\begin{array}{l}
x-4\gt 0\\
x+4\gt 0
\end{array}\right.\quad \Rightarrow x\gt 4\qquad (*)$
in order for the equation to be defined.
LHS: Apply$ \quad\log_{a}(MN)=\log_{a}M+\log_{a}N$
RHS: Apply $\quad \log_{3}3^{2}=2$
$\log_{3}[ (x-4)(x+4)]=\log_{3}9$
... apply the principle of logarithmic equality
$(x-4)(x+4)=9$
$x^{2}-16=9$
$x^{2}=25$
Possible solutions:
$ x=-5\qquad$... does not satisfy (*), not a solution.
$x=5\qquad $... satisfies (*), and is a valid solution.
