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