Logarithms before 1965

Date: 02/08/99 at 16:16:22
From: Nicole
Subject: Logarithmic Use before 1965

Could you tell me how logarithms were used before the year 1965?  

Date: 02/09/99 at 08:45:33
From: Doctor Peterson
Subject: Re: Logarithmic Use before 1965

I'm not sure where the date 1965 comes from, but I suspect it's being 
taken to represent the beginning of electronic calculators. I was in 
high school not long after 1965, and calculators didn't exist as far 
as I was concerned; when I entered college in 1970, every engineering 
student still needed a slide rule. 

We learned how to use logarithms in at least two ways. First, we had 
tables of logarithms that we used to simplify complex multiplication 
problems. For instance, in a simple case you would look up the 
logarithms of the numbers you want to multiply; then you would add the 
logarithms and look up in reverse to find the number whose logarithm 
that was, which gave the answer. There were also tables of logarithms 
of trigonometric functions, so you could save a table lookup when you 
had to multiply. You had to learn a lot of tricks to use logarithms, 
such as how to look up a number between two numbers in the table 
(interpolation), and how to figure the log of any number from a table 
that gave logs only for numbers from 1 to 10.

Second, the slide rule is based on logarithms: the distance of a number 
along the rule is the logarithm of the number, and numbers are 
multiplied by adding those distances.

Calculators mostly eliminated both uses of logarithms. Occasionally, 
it can still be useful to use logs for calculations, when numbers go 
beyond the range of a calculator.

For more information, see this answer on the history of logarithms in 
our archives:

 http://mathforum.org/dr.math/problems/temple.7.12.96.html   

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