Answer
$2$
Work Step by Step
Step 1. Rewrite the equation as $log_{1/3}(x^2+x)=log_{1/3}(x^2-x)-1 \longrightarrow log_{1/3}(x^2+x)=log_{1/3}(x^2-x)-log_{1/3}(1/3)$
Step 2. Thus $x^2+x=3(x^2-x)\longrightarrow 2x^2-4x=0\longrightarrow x=0,2$.
Step 3. Check answers, only $x=2$ fits the original equation.