# Logs by hand?

1. Feb 22, 2007

### 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.

2. Feb 22, 2007

### Staff: Mentor

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

3. Feb 22, 2007

### d_leet

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

4. Feb 22, 2007

### Integral

Staff Emeritus
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.

5. Feb 22, 2007

### Helical

But how were the tables figured out?

6. Feb 22, 2007

### Integral

Staff Emeritus
Last edited by a moderator: Apr 22, 2017
7. Feb 22, 2007

### dextercioby

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

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

8. Feb 22, 2007

### Gib Z

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.

9. Feb 22, 2007

### HallsofIvy

Staff Emeritus
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!

10. Feb 22, 2007

### jing

Last edited by a moderator: Apr 22, 2017
11. Feb 22, 2007

### Integral

Staff Emeritus
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.

12. Feb 22, 2007

### arildno

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

But perhaps more expensive..

13. Feb 22, 2007

### murshid_islam

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