I2.1 If $\log _{2}\left(\log _{4} P\right)=\log _{4}\left(\log _{2} P\right)$ and $P \neq 1$, find the value of $P$.
$\begin{array}{l}\frac{\log \left(\log _{4} P\right)}{\log 2}=\frac{\log \left(\log _{2} P\right)}{\log 4} \\ \frac{\log \left(\log _{4} P\right)}{\log 2}=\frac{\log \left(\log _{2} P\right)}{2 \log 2} \\ 2 \log \left(\log _{4} P\right)=\log \left(\log _{2} P\right) \\ \Rightarrow \log \left(\log _{4} P\right)^{2}=\log \left(\log _{2} P\right) \\ \left(\log _{4} P\right)^{2}=\log _{2} P \\ \left(\frac{\log P}{\log 4}\right)^{2}=\frac{\log P}{\log 2} \\ P \neq 1, \log P \neq 0 \Rightarrow \frac{\log P}{(2 \log 2)^{2}}=\frac{1}{\log 2} \\ \log P=4 \log 2=\log 16 \\ P=16 \\\end{array}$