Question

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log `2 1/4`

Answer 1

Given that log₁₀2 = a and log₁₀3 = b
log `2 1/4`
= log `(9/4)`
= log `(3/2)^2`         
= 2log`(3/2)`                ...[ nlog_am = log_amⁿ ]
= 2( log3 - log2 )         ...[ log_am - log_an = log_a `m/n` ]
= 2( b - a )                   ...[ ∵ log₁₀2 = a and log₁₀3 = b ]
= 2b - 2a