Question

log₁₀ = 0.4771, then find log₁₀ 0.027

Answer 1

Given,

log₁₀3 = 0.4771

log₁₀ 0.027 = log( 27/1000)

= log₁₀ (27 x 10^-3)

= log₁₀ (3³x 10^-3)

= log₁₀(3)³ + log₁₀ (10)^-3

= 3 log₁₀3 – 3 log₁₀10

= 3 x 0.4771 – 3 x 1

= 1.4313 – 3

= – 1.5687

= -2 + 0.4313

= \(\bar{2}\) + 0.4313 = \(\bar{2}\).4313

Hence, log₁₀ 0.027 = 2.4313 or - 1.5687