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Question
Write the following expression as sum or difference of logarithm
In `(("a"^3 ("a" - 2)^2)/sqrt("b"^2 + 5))`
Solution
In `(("a"^3 ("a" - 2)^2)/sqrt("b"^2 + 5))`
= In (a3 (a – 2)2) – In `sqrt("b"^2 + 5)` ...`[log "m"/"n" = log "m" - log "n"]`
= In a3 + In (a – 2)2 – In `("b"^2 + 5)^(1/2)` ...[log mn = log m + log n]
= 3 ln a + 2 ln (a – 2) – `1/2` In (b2 + 5) ...[log mn = nlog m]
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