The equations are:
$\log_{4}(x)+\log_{4}(y)=5$
$\big(\log_{4}(x)\big)\big(\log_{4}(y)\big)=6$
I attempted to solve this problem by solving the pair of equations for $x$.
For the first equation:
$\Longrightarrow \log_{4}(xy)=5 \Longrightarrow xy=4^{5} \Longrightarrow xy=1024 \Rightarrow x=\dfrac{1024}{y}$
For the second equation:
$\Longrightarrow \log{4}(x)=\dfrac{6}{\log_{4}(y)} \Longrightarrow x=4^{\frac{6}{\log_{4}(y)}}$
Then,
$\Longrightarrow \dfrac{1024}{y}=4^{\frac{6}{\log_{4}(y)}}$
How should I move on from here?