Question

If log₁₀ 8 = 0.90, find the value of:

log₁₀ 4

Answer 1

Given that log₁₀8 = 0.90

⇒ log₁₀2 × 2 × 2 = 0.90

⇒ log₁₀2³ = 0.90

⇒ 3log₁₀2 = 0.90

⇒  log₁₀2 = `0.90/3`

⇒  log₁₀2  = 0.30            ...(1)

log 4
= log₁₀( 2 x 2 )
= log₁₀( 2² )
= 2log₁₀2 
= 2( 0.30 )                ...[ from(1) ]
= 0.60