# Solving Logarithms by Hand: A Puzzling Pursuit

• Helical
In summary, people used to solve logarithms by using slide rules and tables, which were calculated using methods such as the Taylor series polynomial. During World War II, people were hired to do these calculations, and at Los Alamos, a number crunching program was used to calculate logarithms until the computer was operational. Mathematician John Napier is credited with the discovery of logarithms, and it is said that scientist John von Neumann memorized log tables.

#### Helical

I'm wondering how people used to solve log's. I can't figure out any sort of pattern when I look at certain logs (to figure out a way to solve them by hand) so any information regarding this would be nice.

I don't mean like log10(100)=2, that's obvious I mean like log10(20)~1.301, how does one figure that out, I asked my math teacher and he couldn't tell me..?

By the way, sorry I don't know how to make subscripts, and thanks.

My guess is that they used slide rules. Have you wiki'ed slide rules yet?

berkeman said:
My guess is that they used slide rules. Have you wiki'ed slide rules yet?

Aren't slide rules based on logarithms? So wouldn't using them to calculate logs be rather circular?

Slide rules and tables. Was a time when the Math CRC was page after page of tables. Both trig functions and logs were read off of tables. You learned to interpolate (linear) between table values in High school.

But how were the tables figured out?

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Helical said:
I'm wondering how people used to solve log's. I can't figure out any sort of pattern when I look at certain logs (to figure out a way to solve them by hand) so any information regarding this would be nice.

I don't mean like log10(100)=2, that's obvious I mean like log10(20)~1.301, how does one figure that out, I asked my math teacher and he couldn't tell me..?

By the way, sorry I don't know how to make subscripts, and thanks.

Any logarithm can be computed by hand, using the Taylor series for $\ln(1\pm x)$ which converges for any real $x<1$ and the logarithm's properties.

For example

$$\ln 243.5 =\ln 0.2435 + 3 \ln 10=\ln 0.2435 + 3 \ln 2 +3\ln 5=\ln 0.2435 + 12 \ln 2+3\ln 5/8$$

There were people, not mathematicians but numerators, who would do these grueling calculations to numerous digits of accuracy. And they got paid a pitence too.

I am told that at Los Alamos, while developing the atomic bomb during world war II, they had a few scientist and hundreds of people who operated adding machines!

John Napier, 1550 and 1617, is credited with the discovery of logarithms

http://johnnapier.com/table_of_logarithms_001.htm"

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HallsofIvy said:
I am told that at Los Alamos, while developing the atomic bomb during world war II, they had a few scientist and hundreds of people who operated adding machines!

The story I heard (Feynman?) is that they had a number crunching program written, but, for reasons I don't recall, the computer was not yet working. So they took the program which consisted of a stack of punch cards each with a single instruction (Some may recall these, I do) and passed it out to a number of people, probably with adding machines, each person did the calculation on their card and passed the result on to the next person.

A human computer.

Integral said:
The story I heard (Feynman?) is that they had a number crunching program written, but, for reasons I don't recall, the computer was not yet working. So they took the program which consisted of a stack of punch cards each with a single instruction (Some may recall these, I do) and passed it out to a number of people, probably with adding machines, each person did the calculation on their card and passed the result on to the next person.

A human computer.

Couldn't they just have plugged those numbers into von Neumann?
That would have been simpler, faster and more reliable.

But perhaps more expensive..

yeah, i have also read that von Neumann memorized the log tables. but how did he do it?