# System of equations with logarithm

Algebra Level 2

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

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