Answer
$x=9$
Work Step by Step
Using properties of logarithms, then,
\begin{array}{l}
\log_3 (x^2-8x)=2\\
x^2-8x=3^2\\
x^2-8x=9\\
x^2-8x-9=0\\
(x-9)(x+1)=0\\
x=\{-1,9\}
.\end{array}
Since the domain of the logarithmic function is the set of all positive numbers, then $
x=9
$.
