Answer
$\{log_35,log_37 \}$
Work Step by Step
Step 1. Let $u=3^x$, we have $u^2-12u+35=0$ or $(u-5)(u-7)=0$
Step 2. For $u=5$, we have $3^x=5$, thus $x=log_35$
Step 3. For $u=7$, we have $3^x=4$, thus $x=log_37$
Step 4. Write the answers in set form $\{log_35,log_37 \}$