While reviewing some old slide rule manuals as a part of participation in some recent threads I also looked at some old calculator manuals. I found the following material on pages 33 and 34 of the manual for the Texas Instruments SR-10:

Quote:For 4 <= a <= 40, the manual prescribes

Logarithmic and Exponential FunctionsThe value of log a can be determined to within +/-0.04% using the square root key. If you repeatedly take the square root of any number, the value will approach unity with a remainder that is proportional to the logarithm of the original number. Because of the eight digit acuracy of the SR-10, the optimum number of times to take the square root is eleven.

1. Enter the value of a.

2. Take the square root eleven times.

3. Subtract 1.

4. Multiply by 889.

The manual gives an example for the common logarithm of 12:

1. Enter 12

2. Take the square root eleven times and see 1.001214

3. Subtract 1 and see 0.001214

4. Multiply by 889 and see 1.079246 which is within 0.006% 0f the correct value of 1.079181.

I haven't been able to locate a reference describing this technique. I thought that I should be able to get there with the use of infinite series but I haven't been able to push that through. Can anyone help?

Palmer