Finding power series representation for ln(5-x).

[lilypetals]

Homework Statement

Find a power series representation for the function and determine the radius of convergence: f(x)=ln(5-x)

Homework Equations

Manipulate into the form 1/(1-x).

The Attempt at a Solution

I know how to do this with other functions, say, x/(9+x²)...
It would convert to x/9 * 1/(1-(-x²/9)), and then you would write the power series as $$\sum$$ (-1)ⁿ * (x²ⁿ⁺¹/9ⁿ⁺¹)
I just don't know how to do this with the natural logarithm involved...any suggestions?

 

[vela]

log (5-x) = log [5(1-x/5)] = log 5 + log (1-x/5)

 

[Slats18]

Have you been told that the radius of convergence for a function is also the radius of convergence for its derivative? Hopefully, if you try that, then you can manipulate your function into one that has a geometric series =)