Respuesta :

Step-by-step explanation:

  1. Assume that [tex]\log _{3}2[/tex] = [tex]\frac{p}{q}[/tex]  ≥ 0    then p and q are positive integers
  2. So, it must comply with  [tex]3^{p} = 2^{q}[/tex]
  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 [tex]\log_{2}3[/tex] is irrational.
  5. Hence proved