Explanation

\(\log_{2} x - \log_{2} y = 2 \implies \log_{2} (\frac{x}{y}) = 2 \)

\(\frac{x}{y} = 2^{2} = 4 \implies x = 4y ... (1)\)

\(\log_{2} (x - 2y) = 3 \implies x - 2y = 2^{3} = 8 ... (2)\)

Putting (1) into (2),

\(4y - 2y = 8 \implies 2y = 8\)

\(y = 4\)

\(x = 4y \implies x = 4(4) = 16\)

\(x = 16 ; y = 4\)

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