Chapter 4 - Mid-Chapter Check Point - Page 479: 14

2

We know that $y=log_{b}x$ is equivalent to $b^{y}=x$ (where $x\gt0$, $b\gt0$, and $b\ne1$). Therefore, $log_{2}(log_{3}81)=log_{2}4=2$. We know that $log_{3}81=4$, because $3^{4}=81$. We know that $log_{2}4=2$, because $2^{2}=4$.