Question

Prove that : `2"log" 15/18 - "log"25/162 + "log"4/9 = log 2 `

Answer 1

We need to prove that
`2"log"15/18 - "log"25/162 + "log"4/9 = log 2`

LHS = `2"log"15/18 - "log"25/162 + "log"4/9`

= `"log"(15/18)^2 - "log"(25/162) + "log"(4/9)`   ....[ nlog_am = log_amⁿ ]

= `"log"[(15/18) xx (15/18)] - "log"25/162 + "log"4/9`

= `"log"(15/18) xx (15/18) xx (4/9) - "log"(25/162)   .....[ log_am + log_an = log_a(mn)]`

= `"log"((15/18) xx (15/18) xx 4/9)/(25/162)    .....[ log_am - log_an = log_a(m/n)]`

= `"log" (15/18) xx (15/18) xx 4/9 xx 162/25`

= `"log" 72/36`
= log 2
= R.H.S.