Question Detail
Question
Solve \( (\log_2 m)^2 - \log_2 m^3 = 10 \).
Correct Answer
Option B is the correct answer.
Detailed Explanation
Let y = log₂ m. Then log₂ m³ = 3 log₂ m = 3y. The equation becomes y² - 3y = 10 => y² - 3y - 10 = 0 => (y-5)(y+2)=0 => y=5 or y=-2. So log₂ m = 5 => m = 2⁵ = 32. log₂ m = -2 => m = 2⁻² = 1/4. So m = 32 or 1/4.
Hint
Substitute y = log₂ m to form a quadratic equation.