A) \[{{\log }_{e}}x\]
B) \[x\]
C) \[{{x}^{-1}}\]
D) \[-{{\log }_{e}}(1+x)\]
Correct Answer: B
Solution :
\[1+\frac{{{\log }_{e}}x}{1\,!}+\frac{{{({{\log }_{e}}x)}^{2}}}{2\ !}+\frac{{{({{\log }_{e}}x)}^{3}}}{3\ !}+......+\frac{{{({{\log }_{e}}x)}^{n}}}{n\ !}+....\] \[={{e}^{({{\log }_{e}}x)}}=x\].
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