5 In this question you may assume that if \(p\) and \(q\) are distinct prime numbers and \(\mathbf { p } ^ { \alpha } = \mathbf { q } ^ { \beta }\) where \(\alpha , \beta \in \mathbb { Z }\), then \(\alpha = 0\) and \(\beta = 0\).

1. Prove that it is not possible to find \(a\) and \(b\) for which \(\mathrm { a } , \mathrm { b } \in \mathbb { Z }\) and \(3 = 2 ^ { \frac { \mathrm { a } } { \mathrm { b } } }\).
2. Deduce that \(\log _ { 2 } 3 \notin \mathbb { Q }\).