Prove that :

log₁₀ 125 = 3(1 - log₁₀ 2)

To prove:

log₁₀ 125 = 3(1 - log₁₀ 2)

Solving R.H.S. of the equation, we get :

⇒ 3(1 - log₁₀ 2)

⇒ 3(log₁₀ 10 - log₁₀ 2)

⇒ 3(log₁₀ $\dfrac{10}{2}$)

⇒ 3 log₁₀ 5

⇒ log₁₀ 5³

⇒ log₁₀ 125

Since, L.H.S. = R.H.S.

Hence, proved that log₁₀ 125 = 3(1 - log₁₀ 2).