# Logs by hand?

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.

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

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?

Integral
Staff Emeritus
Gold Member
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?

Integral
Staff Emeritus
Gold Member
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dextercioby
Homework Helper
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

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

Gib Z
Homework Helper
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.

HallsofIvy
Homework Helper
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!

Integral
Staff Emeritus
Gold Member
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.

arildno
Homework Helper
Gold Member
Dearly Missed
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?