Answer
{$9,-1$}
Work Step by Step
Step 1: $\log_{3} (x^{2}-8x)=2$
Step 2: $(x^{2}-8x)=3^{2}$
Step 3: $(x^{2}-8x)=9$
Step 4: $x^{2}-8x-9=0$
Step 5: $x^{2}+1x-9x-9=0$
Step 6: $x(x+1)-9(x+1)=8$
Step 7: $(x+1)(x-9)=0$
Step 8: $x=-1$ or $x=9$
Therefore, the solution set is {$9,-1$}.