Question

How do you prove `log_2 3` is irrational number ?

Answer 1

See below.

Explanation:

`y = log_2 3 hArr 2^y = 3` If `y` is rational then `y = n/m` with `{n,m} in ZZ` and `m ne 0` or

`2^(n/m) = 3 rArr 2^n = 3^m`

This last equality is an absurd because `3^m` is odd and `2^n` is even.

Concluding `y = log_2 3` is not rational, being then irrational.