Taylor-series of ln(x)

Question

Is it possible to compute the Taylor-series of $\ln(x)$ for $x = 0$. I get $f\prime(x) = \frac{1}{x}$ and by plugging $0$ , it is undefined form.

Answer 1

This is not possible since

$$x\mapsto \ln(x)$$

is not defined at $x=0$.

Though you can develop $\ln(x)$ in terms of $x-1$, and then divide by $x$ to get the development of $\ln(x)/x$ that you said you wanted in the comments.