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Question
Express the following as a single logarithm:
`2"log"(15)/(18) - "log"(25)/(162) + "log"(4)/(9)`
Solution
`2"log"(15)/(18) - "log"(25)/(162) + "log"(4)/(9)`
`2"log"(5)/(2 xx 3) - "log"(5^2)/(2 xx 3^4) + "log"(2^2)/(3^2)`
= 2 log 5 - 2 log 2 - 2 log 3 - {log 52 - log 2 - log 34} + log 22 - log32
= 2 log 5 - 2log 2 - 2log 3 - 2 log 5 + log 2 + 4 log 3 + 2 log 2 - 2 log 3
= log 2.
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