It turns out that the common logarithms of each of the numbers from 2 through 9 can be very well approximated by rational numbers of the form n/40.
Derive each of the numerators with no calculation aids beyond pencil and paper.
We have two competing claims for log 7.
33/40 and 34/40, they are both pretty close but the hard part is now to explain which is better. I am not finished proving it myself but I am pretty sure it can be explained pretty well without a calculator.

Posted by Jer
on 20110601 15:08:08 