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## Main Question or Discussion Point

How were logarithms calculated before the use of calculators.

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How were logarithms calculated before the use of calculators.

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gb7nash

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Assume you want to calculate log

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

1) a

2) a

3) a

If a

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.

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Before electronic pocket calculators became common, every engineering student owned one of these ...How were logarithms calculated before the use of calculators.

http://en.wikipedia.org/wiki/Slide_rule

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HallsofIvy

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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

Instead of taking powers of a number close to 1, as had

Napier, Briggs began with log(10) = 1 and then found other logarithms

by taking successive roots. By finding sqrt(10) = 3.162277 for

example, Briggs had log(3.162277) = 0.500000, and from 10^(3/4) =

sqrt(31.62277) = 5.623413 he had log(5.623413) = 0.7500000.

Continuing in this manner, he computed other common logarithms.

Briggs published his tables of logarithms of numbers from 1 to 1000,

each carried out to 14 places of decimals, in 1617.

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Integral

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Halls post is the answer to how did they generate the tables.

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HallsofIvy

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

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