Reversed Branched logs

Algebra Level 4

{log3(log2x)+log13(log12y)=1xy2=4\begin{cases} \log_3(\log_2x)+\log_{\frac{1}{3}}(\log_{\frac{1}{2}}y)=1 \\ xy^2=4 \end{cases} If the above equations hold for some values of xx and yy, then find the value of xyxy.


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