## College Algebra (10th Edition)

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.