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Log log ln

  1. Apr 8, 2006 #1
    my complex analysis book uses all three of them...

    although i know the difference between log and ln, I'm kinda clueless about Log ... any ideas?
  2. jcsd
  3. Apr 8, 2006 #2
    It's probably the principle value of log. I'm sure your book has it mentioned somewhere.
  4. Apr 8, 2006 #3
  5. Apr 9, 2006 #4


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    In my textbook, log was used to denote the 'old' logarithm for real values only, and Log for the complex logarithm (i.e. Log(z) = log(r) + i*phi, with phi the phase, if I recall correctly).
  6. Apr 10, 2006 #5
    let me tell you how my textbook defines certain terms ...

    log z = ln |z| + i * arg z
    Log z = ln |z| + i * Arg z

    now consider this example:
    log (1+ i * 3^(1/2)
    now the value I would get is ... ln |1+ i * 3 ^(1/2)| + i ( pi/3 + 2 n pi)
    which simplifies to ln 2 + i (pi/3 +2 n pi)

    now the answer in the back of the book is log 2 + i (pi/3 +2 n pi)
    and this is not the first time they have done it ... so i dont think it's a typo ...

    lol ... mind explaning how they replaced ln 2 with log 2??
  7. Apr 10, 2006 #6
    another thing ...
    why do they always use n2pi (n = 0, , 1, -1, 2, -2...)??
    coz the values in case of tangent give the same value for n * pi
  8. Apr 10, 2006 #7
    hmmm... bump?
  9. Apr 10, 2006 #8


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    Your task is to now look up how they define arg and Arg. Most likely, Arg will denote some 'principle branch' and be a single valued function while arg is the multivalued version.

    In advanced textbooks (=beyond intro calculus) "log" usually denotes the base e logarithm, i.e. the "ln" on your calculator. They probably explain this somewhere in your text.
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