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Question
Prove that : `2"log" 15/18 - "log"25/162 + "log"4/9 = log 2 `
Solution
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)` ....[ nlogam = logamn ]
= `"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.
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