System of equations with logarithm

Algebra Level 2

If x=αx=\alpha and y=βy=\beta are solutions to the system of equations 2x24y=7log2(x2)log2y=1,\begin{aligned} 2^x-2\cdot 4^{-y} &=7 \\ \log_2 (x-2)-\log_2 y &=1, \end{aligned} what is the value of 10αβ?10\alpha\beta?

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