Proof for fun, log base 2 of 3 is irrational

Proof for fun, log base 2 of 3 is irrational,
proof by contradiction, more example here:
There are infinitely many primes, https://youtu.be/816JCX5tKD8,
square root of 2 is irrational, https://youtu.be/BhFf0nJ5VOg

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