Discussion:
Deriving natural logarithms
Eugene Griessel
2007-02-01 08:33:45 UTC
Is it possible, even by Newton-Raphson, to derive the natural
logarithm of a number using nothing more than addition, subtraction,
division and multiplication? I would be keen to get an algorithm to
do this - have been trying to derive one myself but with no success.

Eugene L Griessel

A gentleman is a man who knows how to play the saxophone and doesn't.
Eugene Griessel
2007-02-01 13:00:17 UTC
Post by Eugene Griessel
Is it possible, even by Newton-Raphson, to derive the natural
logarithm of a number using nothing more than addition, subtraction,
division and multiplication? I would be keen to get an algorithm to
do this - have been trying to derive one myself but with no success.
Never mind - I have finally figured out an algorithm that works!
Thanks anyway.

Eugene L Griessel

I sometimes think that God in creating man somewhat overestimated
his ability.
Barb Knox
2007-02-01 20:07:35 UTC
Post by Eugene Griessel
Is it possible, even by Newton-Raphson, to derive the natural
logarithm of a number using nothing more than addition, subtraction,
division and multiplication? I would be keen to get an algorithm to
do this - have been trying to derive one myself but with no success.
A common method is to use a power series (e.g. Taylor series).
Post by Eugene Griessel
Eugene L Griessel
A gentleman is a man who knows how to play the saxophone and doesn't.
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| B B a a r b b | altum viditur.
| BBB aa a r bbb |
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Eugene Griessel
2007-02-01 20:11:43 UTC
Post by Barb Knox
Post by Eugene Griessel
Is it possible, even by Newton-Raphson, to derive the natural
logarithm of a number using nothing more than addition, subtraction,
division and multiplication? I would be keen to get an algorithm to
do this - have been trying to derive one myself but with no success.
A common method is to use a power series (e.g. Taylor series).
The Taylor series requires raising numbers to powers IIRC. I have
found an elegantly simple 3 step algorithm that seems to work well -
I have tested it extensively and it gives the results I require!
Thanks. (Personally I have not worked with logs since the 70's! -
computers and calculators seem to have killed the need for most
people!)

Eugene L Griessel

I sometimes think that God in creating man somewhat overestimated
his ability.