A) \[{{\log }_{e}}(1-y)\]
B) \[\frac{1}{{{\log }_{e}}(1-y)}\]
C) \[{{\log }_{e}}\frac{1}{1-y}\]
D) \[{{\log }_{e}}(1+y)\]
Correct Answer: C
Solution :
\[y=x-\frac{{{x}^{2}}}{2\ !}+\frac{{{x}^{3}}}{3\ !}-\frac{{{x}^{4}}}{4\ !}+.......=1-{{e}^{-x}}\] \[\Rightarrow {{e}^{-x}}=1-y\Rightarrow -x={{\log }_{e}}(1-y)\Rightarrow x={{\log }_{e}}\frac{1}{1-y}\].
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