Question

Prove that log ₁₀ 125 = 3 (1 - log ₁₀ 2)

Answer 1

L.H.S.
= log ₁₀ 125
= `"log"_10 (1000/8)`
= log ₁₀ 1000 - log ₁₀ 8
= log ₁₀ (10)³ - log₁₀(2)³
= 3log ₁₀ 10 - 3log ₁₀ 2
= 3 x 1 - 3log₁₀ 2
= 3(1 - log ₁₀ 2)
= R.H.S.