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In the expansion of 2 log(n) x- log(n)...

In the expansion of ` 2 log_(n) x- log_(n) (x+1) - log_(e)(x-1),` the coefficient of `x^(-4)` is

A

`1/2`

B

-1

C

1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
a
` 2log_(e)x- log_(e){(1+1/x)xx}-log_(e){(1-1/x)x}`
` = 2 log_(e)x - {log_(e)(1+1/x)+log_(e)x}-{log_(e)(1-1/x)+log_(e)x}`
` = - { log_(e) (1+1/x)+log_(e)(1-1/x)}`
` = - { log_(e)(1+1/x)+log_(e)(1-1/x)}`
` =2 {1/(2x^(2))+1/(4x^(4))...}`
` :. "The coefficient of " x^(-4) = 2xx 1/4 =1/2`
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