Question 32877: Show that log5(8) is irrational.
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! Prove log5 8 = p/q for some positive integer p,q with no commond divisor.
(i.e p/q in reduced form)
then 5^(p/q) = 8 and so 5^p = 8^q.
But the left hand side is odd , while the right hand side is even.
This impossible.
Hence, log5 8 must be an irrational.
Suggest: try to prove sqrt(2) or sqrt(3) are irrat.
Kenny
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