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.

(In reply to Who is right for 7? by Jer)

Both are approximations, so neither is exactly right!

log(7) = 0.845  ;  33/40 = 0.825  ;  34/40 = 0.850

So, 33/40 is a tad closer.

Take your pick!    :-)

Posted by JayDeeKay on 2011-06-01 18:41:41