Hur får man detta gränsvärde

$$\begin{gathered} \underset{y\to b}{\lim }\frac{y-b}{\ln y -\ln b}=\underset{y\to b}{\lim }\frac{y-b}{\ln {\displaystyle \frac{y}{b}}}=\underset{y\to b}{\lim }\frac{y-b}{\ln ({\displaystyle \frac{y-b}{b}}+1)}= \\ =\underset{y\to b}{\lim }\frac{1}{{\displaystyle \frac{1}{b}\frac{\ln ({\displaystyle \frac{y-b}{b}}+1)}{{\displaystyle \frac{y-b}{b}}}}}=\frac{1}{1/b}=b \end{gathered}$$

Smutsmunnen skrev:

$$\begin{gathered} \underset{y\to b}{\lim }\frac{y-b}{\ln y -\ln b}=\underset{y\to b}{\lim }\frac{y-b}{\ln {\displaystyle \frac{y}{b}}}=\underset{y\to b}{\lim }\frac{y-b}{\ln ({\displaystyle \frac{y-b}{b}}+1)}= \\ =\underset{y\to b}{\lim }\frac{1}{{\displaystyle \frac{1}{b}\frac{\ln ({\displaystyle \frac{y-b}{b}}+1)}{{\displaystyle \frac{y-b}{b}}}}}=\frac{1}{1/b}=b \end{gathered}$$

Jag förstår. Tack för hjälpen.