Solve \((\log_{2} m)^{2} - \log_{2} m^{3} = 10\).

Explanation

\((\log_{2} m)^{2} - \log_{2} m^{3} = 10\)

Let \(\log_{2} m\) = x.

\((\log_{2} m)^{2} - 3\log_{2} m - 10 = 0\)

\(\implies x^{2} - 3x - 10 = 0\)

\(x^{2} + 2x - 5x - 10 = 0 \)

\(x(x + 2) - 5(x + 2) = 0\)

\(\implies x = \text{-2 or 5}\)

When \(\log_{2} m = -2 \implies m = 2^{-2} = \frac{1}{4}\)

When \(\log_{2} m = 5 \implies m = 2^{5} = 32\).