Question

If log₁₀ 8 = 0.90; find the value of : log 0.125

Answer 1

Given that log₁₀8 = 0.90

⇒ log₁₀2 x 2 x 2 = 0.90

⇒ log₁₀2³ = 0.90

⇒ 3log₁₀2 = 0.90

⇒  log₁₀2 = `0.90/3`

⇒  log₁₀2  = 0.30            ...(1)

log 0.125

= log₁₀`125/1000`

= log₁₀`1/8`

= `log_10 (1/(2 xx 2 xx 2))`

= `log_10(1/2^3)`

= log₁₀2^-3 
= - 3 x ( 0.30 )          [ from(1) ]
= - 0.9