Maharashtra State BoardHSC Science (Electronics) 11th
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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))`

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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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