Prove by contradiction Watch
Prove by contradiction that log23 is irrational.
thanks in advance
log_2(3) = m/n
But then 3 = 2^(m/n) so 3^n = 2^m. This is impossible, as the LHS is odd while the RHS is even. We have deduced a contradiction, hence our original assumption must be false. Therefore log_2(3) is irrational.