Question

If log₁₀ 8 = 0.90; find the value of : log√32

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 √32
=`log_10(32)^(1/2)`

= `1/2 log_10(32)`

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

= `1/2 log_10(2^5)`

= `1/2 xx 5log_10 2`

= `1/2 xx 5( 0.30 )`           [ from(1) ] 

= 5 x 0.15
= 0.75