# Write the following expression as sum or difference of logarithm In (a3(a-2)2b2+5) - Mathematics and Statistics

Sum

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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