Question

Prove that log3(2) is irrational.

Answer 1

Explanation:

1. Assume that
   `\log _(3)2` =
   `(p)/(q)` ≥ 0 then p and q are positive integers
2. So, it must comply with
   `3^(p) = 2^(q)`
3. If p and q are positive (≥ 0), then LHS is odd and RHS is even which is a clear contradiction.
4. This shows that
   `\log_(2)3` is irrational.
5. Hence proved