Series expansion of logarithmic function

1. Aug 15, 2011

seboastien

1. The problem statement, all variables and given/known data
Find first three non zero terms in series expansion where the argument of funstion is small

ln(5+p)

2. Relevant equations

3. The attempt at a solution

The only way I could think how to do this is by saying ln(5+p) = ln(1+(4+p)) and expanding to

(4+p)- 1/2(4+p)^2 + 1/3(4+p)^3 - .... however, I imagine that this would only work if p was approx -4.

2. Aug 15, 2011

seboastien

Come on guys! I really need to know how to do this!

3. Aug 15, 2011

HallsofIvy

Staff Emeritus
Well, the accuracy, for any finite polynomial expansion, deteriorates as p gets farther from -4 but is the accuracy really relevant? You are only asked to "Find first three non zero terms".

4. Aug 15, 2011

seboastien

How do I find the first three non-zero terms of ln(5+p), I'm pretty sure that my answer is wrong.

5. Aug 15, 2011

dynamicsolo

You'll want to write this as ln( 5 [ 1+(p/5) ] ) ; then use the properties of logarithms to write it as two terms, one of which is the term you would do the series expansion for.

6. Aug 15, 2011

Thank you