Question

$\lim\limits _{x\to 1 } \left(log \,ex\right)^{1/log\,x}$ is equal

• A. $e^{-1}$
• B. $e$
• C. $e^2$
• D. $0$

Answer 1

Answer: (B)

$e$

Answer 2

$\displaystyle\lim _{x \rightarrow 1}(\log e x)^{1 / \log x}=\displaystyle\lim _{x \rightarrow 1}[\log e+\log x]^{1 / \log x}$ $= \displaystyle\lim _{x \rightarrow 1}[1+\log x]^{1 / \log x}$ $=e^{\displaystyle\lim _{x \rightarrow 1} \frac{\log x}{\log x}}=e$