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Question on Logarithms

  1. Jun 25, 2011 #1
    How were logarithms calculated before the use of calculators.
     
  2. jcsd
  3. Jun 25, 2011 #2

    gb7nash

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    Here's an iterative method to approximate it. For instance:

    Assume you want to calculate logab, where a and b are positive numbers. So you want to find x such that ax = b. From visual inspection, pick a point y so that you're sure that ay < b and a point z so that az > b.

    Now consider w = (y+z)/2 (which is the midpoint between y and z). One of three things will happen:

    1) aw < b

    2) aw > b

    3) aw = b

    If aw < b, take the midpoint between w and z and repeat. If aw > b, take the midpoint between w and y and repeat. If aw = b, then you're done(though this will probably not happen).

    Keep repeating until you're within a certain epsilon of b.

    _____

    You can also look at the taylor series expansion around a certain point and cut it off past a certain point. This might be more work though.
     
  4. Jun 26, 2011 #3
    Before electronic pocket calculators became common, every engineering student owned one of these ... powerlog.jpg

    http://en.wikipedia.org/wiki/Slide_rule
     
  5. Jun 26, 2011 #4

    HallsofIvy

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    Yes, but you needed to know the value of the logarithms in order to make a slide rule.

    I can't speak for what was done historically, but you could use the Taylor's series for the logarithm:
    [tex]ln(x)= \sum_{n=1}^\infty \frac{(-1)^{n-1}}{n}(x- 1)^n[/tex]

    Ahh!
    On "Math Forum- Ask Dr. Math"
    http://mathforum.org/library/drmath/view/52469.html
    they have
     
  6. Jun 26, 2011 #5

    Integral

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    If you needed more then the 3 digit accuracy of a slide rule you opened a book of log tables. We were even taught to do a linear interpolation to get values between tabulated values.

    Halls post is the answer to how did they generate the tables.
     
  7. Jun 26, 2011 #6

    HallsofIvy

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    Oh, dear! You are showing your age!

    Yes that's how we did it in the years "B.C.".


    (Before Calculators)
     
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