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Question

loge(1+3x)(1-2x) is equal to


A

-5x5x2235x33

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B

-5x+5x2235x33+

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C

5x5x22+35x33

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D

5x+5x22+35x33+

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Solution

The correct option is C

5x5x22+35x33


Explanation for the correct option:

Finding loge(1+3x)(1-2x)is equal to :

Given : loge(1+3x)(1-2x)

loge(1+3x)(1-2x)=log(1+3x)loge(1-2x)[logab=logalogb]ln(1+x)=x-(x22)+(x33)-.............+(-1)n-1(xnn)+...........ln(1-x)=-x-(x22)-(x33)-............-(xnn)-...........log(1+3x)loge(1-2x)=3x-(3x)22+(3x)33-..--2x(2x)22(2x)33-=3x-(3x)22+(3x)33-..+2x+(2x)22+(2x)33+=5x5x22+35x33-

Hence the correct answer is option (C)


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