Etymology of 'Logarithm'

Date: 03/19/99 at 18:31:08
From: Marco Filipetto
Subject: About logarithms

Why is a 'logarithm' called a 'logarithm'? Where did the term originate? 
Also, why is the inverse of the exponential function called a 'logarithm'? 

We thought that logarithms had to be tabled or 'logged' (as in Star Trek 
log) in charts, and thus the name 'logarithm'.

Thanks.

Date: 03/19/99 at 21:03:30
From: Doctor Rick
Subject: Re: About logarithms

The word 'logarithm' was coined by John Napier, the inventor of a form 
of logarithm, in 1614. See

   Earliest Known Uses of Some of the Words of Mathematics
   http://members.aol.com/jeff570/mathword.html   

It comes from the Greek words 'logos' and 'arithmes'. The second word 
means 'number'. The first word has a broad range of meanings, starting 
from 'word' or 'speech' (thus our word 'dialog'), going into 'thought' 
and 'reason' (thus 'logical'), and on to 'proportion'. In this range of 
meanings, it resembles the Latin 'ratio', which means both 'reason' and 
'proportion' (thus the two meanings of 'rational': reasonable, and 
expressable as a ratio or proportion of two integers).

Thus, a 'logarithm' is a 'proportion number'. I suppose the thinking 
was that logarithms help in the calculation of proportions: instead of 
multiplying a number by a fraction, you just add or subtract the 
logarithm of the fraction to the logarithm of the number.

The logarithm actually predates the exponential function, one of the 
oddities of math history. 'Exponent' is Latin for 'putting out'; I 
will have to think a bit about why it might be called that.

I wondered briefly if 'log' as in logbook had to do with the logos 
part, at least -- but then I remembered the nautical origin of 'log'. 
To measure a ship's speed, sailors would heave a log, attached to a rope, 
into the water. The rope had knots in it, and a sailor would count the 
knots that passed through his hands in a certain amount of time. The 
record of speed and position came to include other information, but 
it was still called the log book. And you can guess that the unit of 
speed, a knot (nautical mile per hour), also came out of this practice.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/