Question

solve:${lim}_{x\to 7}\frac{\log x-\log 7}{x-7}$

Answer 1

Considering the question to be:

$f\left(x\right)=\frac{\log x-\log 7}{x-7}$

${lim}_{x\to 7}\frac{\log x-\log 7}{x-7}$

Apply L-Hospital's rule

${lim}_{x\to 7}\frac{\frac{1}{x}}{1-0}$

${lim}_{x\to 7}\frac{1}{x}$

$\frac{1}{7}$