If the fourth term in the expansion of `{sqrt(1/(""_"x^log(x+1)"}'+1/(x^12)}^6 is equal to `200 and x >1,` then find x

Explanation

Given expansion is,

`(sqrt(1/(x^(log(x+1))))+x^(1/12)`

Fourth term in the given expansion can be given as,

`T_4 = C(6,3)(sqrt(1/(x^(log(x+1)))))^3*(x^(1/12))^3`

`=>200 = 20(x^(1/(logx+1)))^(3/2)x^(1/4)`

`=>10 = x^(3/(2(logx+1))+1/4)`

`=>x^(log_x 10) = x^(3/(2(logx+1))+1/4)`

`=>log_x 10 = 3/(2(logx+1))+1/4`

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