\[{{\log }_{e}}x-{{\log }_{e}}(x-1)=\]

1.	\[{{\log }_{e}}x-{{\log }_{e}}(x-1)=\]
A.	\[\frac{1}{x}-\frac{1}{2{{x}^{2}}}+\frac{1}{3{{x}^{3}}}-.....\infty \]
B.	\[\frac{1}{x}+\frac{1}{2{{x}^{2}}}+\frac{1}{3{{x}^{3}}}+.....\infty \]
C.	\[2\,\left( \frac{1}{x}+\frac{1}{3{{x}^{3}}}+\frac{1}{5{{x}^{5}}}+...\infty \right)\]
D.	\[2\,\left( \frac{1}{x}-\frac{1}{3{{x}^{3}}}+\frac{1}{5{{x}^{5}}}-...\infty \right)\]
Answer» C. \[2\,\left( \frac{1}{x}+\frac{1}{3{{x}^{3}}}+\frac{1}{5{{x}^{5}}}+...\infty \right)\]

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\[{{\log }_{e}}x-{{\log }_{e}}(x-1)=\]

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