[MP PET 2002]
A) $ {\log_{e}}3 $
B) 0
C) 1
D) $ f(x) $
Correct Answer: D
$ \underset{x\to 0}{\mathop{\lim }},\frac{{\log_{e}}(1+x)}{3^{x}-1} $ , $ ( \frac{0}{0},\text{ form} ) $ 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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