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} – 3log_{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).