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 2011-06-01 15:08:08