Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.3 - Page 477: 91

False; $log_{4}(2x)^{3}=3log_{4}(2x)$

We are given that $log_{4}(2x^{3})=3log_{4}(2x)$. According to the power rule of logarithms, we know that $log_{b}M^{p}=plog_{b}M$ (when $b$ and $M$ are positive real numbers, $b\ne1$, and $p$ is any real number). Therefore, $log_{4}(2x)^{3}=3log_{4}(2x)$. The given statement is false.