Theory question 101
Indices and LogarithmsSolve (log2m)2 − log2m3 = 10.
Show the model answer
Model answer
Let p = log₂m: p² − 3p − 10 = 0, (p − 5)(p + 2) = 0.
p = 5: m = 2⁵ = 32.
p = −2: m = 2⁻² = ¼.
Explanation
log m³ = 3 log m turns it into a quadratic.