Question

If log₁₀2 = a and log₁₀3 = b; express each of the following in terms of 'a' and 'b' :  log `3 1/8`

Answer 1

log `3 1/8`

= `log_10( 25/8 xx 4/4 )`

= `log_10( 100/32 )`

= `log_10 100 - log_10 32    ...[ log_a(m/n) = log_a m - log_a n ]`
= `log_10 100 - log_10 2^5 `
= 2 - log₁₀2⁵              ...[ ∵ log₁₀100 = 2 ]
= 2 - 5log₁₀2             ...[ log_amⁿ = nlog_am ]
= 2 - 5a                     ...[ ∵ log₁₀2 = a ]