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?
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! :-)