Question

Prove that log3(2) is irrational.

Answer 1

Step-by-step explanation:

1. Assume that $\log _{3}2$ = $\frac{p}{q}$  ≥ 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