How to represent $\ln(5-x)$ as a power series?

Question

I know that $$ \ln(1+x)=\sum _{n=1}^{\infty }\:\left(-1\right)^{n-1}\frac{x^{n}}{n} $$

Answer 1

Hint: $$\ln(5-x)=\ln\left[5\left(1-\frac{x}{5}\right)\right]=\ln 5+\ln\left(1-\frac{x}{5}\right). $$

Answer 2

In your case it's more convenient to use $$ \log \bigg( \frac{1}{1-w} \bigg) = \sum_{k=1}^{n} \frac{w^k}{k} $$ just multiply by $-1$ and set $w=5x$.