Question

Simplify to the extent possible: (
logx16)(log2 x)

Answer 1

Use the change-of-base property for logarithms to write

logₓ(16) log₂(x) = (ln(16) / ln(x)) (ln(x) / ln(2)) = ln(16)/ln(2) = log₂(16)

Then since 2⁴ = 16, we hvae

log₂(16) = log₂(2⁴) = 4 log₂(2) = 4