Question

Prove that Log3 (11) is irrational

Answer 1

Answer:

Proof by contradiction:

Let log 5 at base 3 is rational, say a/b where

a and b are positive integers(check that a/b has to be positive).

So

3a/b=5

3a=5b

Therefore 3 must divide 5.

But 3 and 5 are co-prime.

So, our assumption is wrong.

Hence it is irrational.

Step-by-step explanation:

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