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log (e). (1+3x)/(1-2x) is equal to...

` log _(e). (1+3x)/(1-2x)` is equal to

A

` -5x -(5x^(2))/2 - (35x^(3))/3-...`

B

` -5x + (5x^(2))/2 - (35x^(2))/3 +....`

C

` 1-4 log_(e) 2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
c
` log_(e) ((1+3x)/(1-2x))=log_(e)(1+3x)-log_(e)(1-2x)`
` = [ 3x-(3x)^(2)/2 +(3x)^(3)/3-...]+[2x+(2x)^(2)/2 +(2x)^(3)/3 +...]`
`5x - (5x^(2))/2 +(35x^(3))/3-...`
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