Question

$\underset{x\to e}{lim}\frac{\log x-1}{x-e}$ is equal to

• A. $e$
• B. $\frac{1}{e}$
• C. $1$
• D. $0$

Answer 1

The correct option is B $\frac{1}{e}$

Given,

${lim}_{x\to e}\left(\frac{\log \left(x\right)-1}{x-e}\right)$

apply L - Hospital's rule,

$={lim}_{x\to e}\left(\frac{\frac{1}{x}}{1}\right)$

$={lim}_{x\to e}\left(\frac{1}{x}\right)$

$=\frac{1}{e}$