Answer
$x=\dfrac{\ln{14}}{\ln{3}} \approx 2.402$
Work Step by Step
Take the $\log_3$ of both sides:
$\log_3{(3^x)}=\log_3{14}\\x=\log_3{14}$
We know that $\log_a {b}=\dfrac{\log_c {b}}{\log_c {a}}$ (Change of Base formula).
Use a calculator and the change-of-base rule above to obtain
$x=\log_3{14}=\dfrac{\ln{14}}{\ln{3}}\approx2.402$
