In the expansion of 2logex–loge(x+1)–loge(x-1) the coefficient of x-4is:
12
-1
1
None of these
Determine the coefficient of x-4
We can rewrite the (x+1)as1+1xxand(x-1)as1-1xx, therefore on substituting we have,
⇒2logex-loge1+1xx–loge1-1xx⇒2logex–loge1+1x+logex–loge1-1x+logex∵logab=loga+logb⇒-loge1+1x-loge1+-1x⇒-1x-12x2+13x3-14x4+.......+-1x-12x2-13x3-14x4-.......∵log(1+a)=a-a22+a33-a44+..........⇒14x4+14x4[Neglectingotherterms]⇒12x-4Hence, option A is the correct answer.