Answer
false
Work Step by Step
RECALL:
$\log_a{B^r} = r \cdot \log_a{B}$
The given expression is $\log_2{(3x^4)}=4\cdot\log_2{(3x)}$
Notice that the exponent $4$ in $(3x^4)$ applies only to $x$ but not to $3$.
Thus, the rule above cannot be applied, which means that the exponent $4$ cannot be brought outside the logarithm.
The rule above can only be applied if the given expression was $\log_2{(3x)^4}$.
Thus, the given statement is false.
