# System of equations with logarithm

Algebra Level 2

If $$x=\alpha$$ and $$y=\beta$$ are solutions to the system of equations \begin{align} 2^x-2\cdot 4^{-y} &=7 \\ \log_2 (x-2)-\log_2 y &=1, \end{align} what is the value of $$10\alpha\beta?$$

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