Answer
$2$
Work Step by Step
Step 1. Combine the left side to get $log_3[(x+1)(2x-3)]=1$, thus $(x+1)(2x-3)=3^1$
Step 2. Solve the above equation $2x^2-x-6=0\longrightarrow (x-2)(2x+3)=0 \longrightarrow x=-\frac{3}{2}, 2$
Step 3. Check, only $x=2$ fits the original equation.