Question

Show that log 5 is irrational.

Answer 1

Let log5 at base 3= p/q
5=3^p/q....where p and q are integers (q isnot equals to zero).
5^q=3^p
As 5 and 3 are prime numbers. There is no integers multiple of 5 equals 3 and vice versa. Therefore this is a contradiction (p and q are integers).