How do you prove log_2 3 is irrational number ?

1 Answer
Oct 27, 2017

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.