Question

Find the lim [(ln(x+5) - ln5) / x ] as x approaches 0
...?

Answer 1

Use
`\lim_(x \to 0)( ln(( 1+x )))/(x)=1`


`\lim_(x \to 0)(\ln(x+5) - \ln5)/(x) \\ \\ \lim_(x \to 0)\frac{ \ln{ (x+5)/(5) }}{x} \\ \\ \lim_(x \to 0)\frac{ \ln{( 1+(x)/(5) )}}{x} \\ \\ \lim_(x \to 0)\frac{ \ln{( 1+(x)/(5) )}}{(x)/(5)* 5} \\ \\ (1)/(5) \lim_(x \to 0)\frac{ \ln{( 1+(x)/(5) )}}{(x)/(5)} \\ \\ (1)/(5) * 1 \\ \\(1)/(5)`