Logarithm

$\log_2(\log_3x)=\log_3(\log_2x) \rightarrow \text{ apply change of base to } \log_3 \text{ on both sides and change to } \log_2 \text{.}$

$\log_2(\frac{\log_2x}{\log_23})=\frac{\log_2(\log_2x)}{\log_23}$

$\log_2(\log_2x) - \log_2({\log_23})=\frac{\log_2(\log_2x)}{\log_23}$

$\log_2(\log_2x) \rightarrow z \; \log_23 \rightarrow y$

$z-\log_2y=\frac{z}{y}$

$z=\frac{y\log_2y}{y-1}$

$x=2^{2^{\frac{(\log_23)(\log_2(\log_23))}{\log_2{3}-1}}}$

I agree - 2^2 is 4, by the way