Question

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log 2.25

Answer 1

log₁₀2 = a and log₁₀3 = b
log 2.25

= log`225/100`

= log`[25 xx 9 ]/[ 25 xx 4 ]`

= log`[25 xx 9 ]/[ 25 xx 4 ]`

= log`(9/4)`

= `log (3/2)^2`

= `log (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