For the following function, find the Taylor series centered at $x=3$ and give the first 5 nonzero terms of the Taylor series. Write the interval of convergence of the series.

$$f(x) =\ln(x)$$

$f(x) =$ $+ \displaystyle\sum\limits_{n=1}^{\infty}$

$f(x) =$ $+$ $+$ $+$ $+$ $+ \cdots$

The interval of convergence is: (Give your answer in interval notation.)