Answer
$\text{false}$
Work Step by Step
Recall:
\begin{align*}
&(1)\quad \log_a{MN}=\log_a{M}+\log_a{N}\\
&(2)\quad \log_a{x^r}=r\log_a{x}
\end{align*}
Thus, applying the rules above to the given expression gives:
\begin{align*}
\log _{2}\left(3 x^{4}\right)&=\log _{2} 3+\log _{2}\left(x^{4}\right)\\
&=\log _{2} 3+4 \log _{2} x\\
\end{align*}
Note that
$$\log _{2} 3+4 \log _{2} x\neq 4 \log _{2}(3 x)$$
Therefore the given statement is false.
