Question

${lim}_{x\to 0}\frac{log(2+x)+log0.5}{x}$

Answer 1

${lim}_{x\to 0}\frac{log(2+x)+log0.5}{x}$

$={lim}_{x\to 0}\frac{log(2+x)+log\frac{1}{2}}{x}$

$={lim}_{x\to 0}\frac{log(1+\frac{x}{2})}{2\left(\frac{x}{2}\right)}$

$=\frac{1}{2}$