Answer
$\text{Exact: } \dfrac{\ln 14}{\ln 3}$
$\text{Approximately: } 2.402$
Work Step by Step
$\because a^y = b \text{ is equivalent to } y = \log_a b$
$\therefore 3^{x}=14 \text{ is equivalent to } x = \log_3 14$
Solve the equation above using the Change of Base Formula, which is $\hspace{20pt} \log_ a M = \dfrac{\log_b M}{\log_b a}$, to obtain:
$x=\log_3 14 \\\\
x= \dfrac{\ln 14}{\ln 3}$
Therefore,
$ x = \boxed{\dfrac{\ln 14}{\ln 3} \approx 2.402}$
