Answer
$x=\{ -2,4 \}$
Work Step by Step
Since $y=b^x$ is equivalent to $\log_b y=x$, then the given equation, $
\log_8 (x^2-2x)=1
,$ is equivalent to
\begin{array}{l}\require{cancel}
x^2-2x=8^1
.\end{array}
Using concepts of quadratic equations, the solutions to the equation above are
\begin{array}{l}\require{cancel}
x^2-2x=8
\\\\
x^2-2x-8=0
\\\\
(x-4)(x+2)=0
\\\\
x=\{ -2,4 \}
.\end{array}
Upon checking, both solutions satisfy the original equation. Hence, $
x=\{ -2,4 \}
.$
