Can you remove the log?

Algebra Level 4

{(3x)log3=(4y)log44logx=3logy\large\begin{cases} (3x)^{\log 3} = (4y)^{\log 4}\\ 4^{\log x}= 3^{\log y}\end{cases}

Given the system of equations above, find the value of 1x+1y \dfrac{1}{x}+\dfrac{1}{y} .

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