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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