Answer
$x=-2$ and $x=4$
Work Step by Step
$\log_{8}(x^{2}-2x)=1$
Rewrite in exponential form:
$8^{1}=x^{2}-2x$
$x^{2}-2x=8$
Take the $8$ to the left side of the equation":
$x^{2}-2x-8=0$
Solve this equation by factoring:
$(x+2)(x-4)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x+2=0$
$x=-2$
$x-4=0$
$x=4$
The initial equation is not undefined for either of the solutions found. The answer is $x=-2$ and $x=4$
