Answer
$x=9$
Work Step by Step
$\log_{3}x+\log_{3}(x-8)=2$
Combine $\log_{3}x+\log_{3}(x-8)$ as a the $\log$ of a product:
$\log_{3}x(x-8)=2$
$\log_{3}(x^{2}-8x)=2$
Rewrite in exponential form:
$3^{2}=x^{2}-8x$
$x^{2}-8x=9$
$x^{2}-8x-9=0$
Solve this equation by factoring:
$(x+1)(x-9)=0$
Set both factors equal to $0$ and solve each individual equation for $x$:
$x+1=0$
$x=-1$
$x-9=0$
$x=9$
The original equation is undefined for $x=-1$, the answer is just $x=9$
