Can you solve this log proof?

Question

prove by contraidiciton that log 3 cannot be written in the form (m/n) where m and n are positive integers

Answer 1

log3=m/n
3=10^(m/n)

which is impossible (as 3 is prime)

therefore log3 cannot be written in the form (m/n) where m and n are positive integers

this probably isn't a 'proof' proof, but it is in my mind :)

Answer 2

I answered this same question yesterday, but here it goes:

If log(3) = m/n, then 3 = 10^(m/n), and 3^n = 10^m. But if m and n are integers, then 3^n is always going to be odd and 10^m is always going to be even. So they can't be the same.

Answer 3

http://www.yorku.ca/math1190/Q2BS.pdf
first question gives proof by contradiction that log(base5)3 is irrational - maybe you can extend this to whatever base you happen to be working in.