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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