Prove the following:

log₁₀25+ log₁₀4 = log₅25

Given,

log₁₀25+ log₁₀4 = log₅25

Simplifying L.H.S. we get,

⇒ log₁₀25+ log₁₀4 = log₁₀(25 × 4)

= log₁₀100

= log₁₀10²

= 2log₁₀10 = 2.

Simplifying R.H.S. we get,

⇒ log₅25 = log₅5²

= 2log₅5

= 2(1) = 2.

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

Hence, proved that log₁₀25+ log₁₀4 = log₅25.