Finding function from the power series $\sum_{n=1}^{+\infty} \frac{3^{n-1}}{4^n \cdot n}$

Question

I have to find sum of series $$\sum_{n=1}^{+\infty} \frac{3^{n-1}}{4^n \cdot n}$$

The hint is to find a function whose power series at some point is equal to the given series.

I am struggling with finding such a function.

One the one hand I have

$$f(x) = \sum_{n=0}^{+\infty} \frac{f^{(n)}(x_0)}{n!}(x-x_0)^n$$

And on the other hand I have series in this form

$$\sum_{n=0}^{+\infty}c_n(x-x_0)^n$$

How do I find such $f(x)$ and point $x_0$ from the equations above?

Would be grateful for any hints.