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Series expansion of logarithmic function

  1. Aug 15, 2011 #1
    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. jcsd
  3. Aug 15, 2011 #2
    Come on guys! I really need to know how to do this!
     
  4. Aug 15, 2011 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    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".
     
  5. Aug 15, 2011 #4
    How do I find the first three non-zero terms of ln(5+p), I'm pretty sure that my answer is wrong.
     
  6. Aug 15, 2011 #5

    dynamicsolo

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    Homework Helper

    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.
     
  7. Aug 15, 2011 #6
    Thank you
     
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