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Question
Express the following as a single logarithm:
`"log"(81)/(8) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(25)/(9)`
Solution
`"log"(81)/(8) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(25)/(9)`
= `"log"(3^4)/(2^3) - 2"log"(3)/(5) + 3"log"(2)/(5) + "log"(5^2)/(3^2)`
= log34 - log23 - 2log3 + 2log5 + 3log2 - 3log5 + log52 - log32
= 4log3 - 3log2 - 2log3 + 2log5 + 3log2 - 3log5 + 2log5 - 2log3
= log5.
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