I1.2 Find the value of $b$ if $\log _{2}\left\{\log _{2}\left[\log _{2}(2 b)+a\right]+a\right\}=a$.
$\begin{array}{l}\log _{2}\left\{\log _{2}\left[\log _{2}(2 b)+2\right]+2\right\}=2 \\ \log _{2}\left[\log _{2}(2 b)+2\right]+2=2^{2}=4 \\ \log _{2}\left[\log _{2}(2 b)+2\right]=2 \\ \log _{2}(2 b)+2=2^{2}=4 \\ \Rightarrow \log _{2}(2 b)=2 \\ 2 b=2^{2}=4 \\ \Rightarrow b=2\end{array}$