Answer
{$\frac{3e^{2}}{e^{2}-3}$}
Work Step by Step
Step 1: $\ln 3x-\ln (x-3)=2$
Step 2: $\ln \frac{3x}{x-3}=2$
Step 3: $\frac{3x}{x-3}=e^{2}$
Step 4: $3x=e^{2}(x-3)$
Step 5: $3x-e^{2}x=-3e^{2}$
Step 6: $x(3-e^{2})=-3e^{2}$
Step 7: $x=\frac{-3e^{2}}{(3-e^{2})}$
Step 8: $x=\frac{3e^{2}}{e^{2}-3}$
Therefore, the solution set is {$\frac{3e^{2}}{e^{2}-3}$}.
