A) \[{{\log }_{e}}3\]
B) 0
C) 1
D) \[f(x)\]
Correct Answer: D
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{\log }_{e}}(1+x)}{{{3}^{x}}-1}\], \[\left( \frac{0}{0}\,\text{ form} \right)\] Using L-Hospital?s rule, \[\underset{x\to 0}{\mathop{\lim }}\,\frac{\frac{1}{1+x}}{{{3}^{x}}{{\log }_{e}}3}=\frac{1}{{{\log }_{e}}3}={{\log }_{3}}e\].
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