prove log base 2 of 3 is irrational
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Originally Posted by teramaries prove log base 2 of 3 is irrational Now look at the prime factorization of both sides and see this forces which is absurd in our case.
Originally Posted by teramaries prove log base 2 of 3 is irrational Use proof by contradiction. Assume where p and q are co-prime positive whole numbers . Now consider the last digits of and to get the required contradiction.
A slight variation of previous proofs . . . Assume where and are coprime positive integers. Then: . Since is a positive integer, is even. Since is a positive integer, is odd. Hence: . . . Q.E.D.
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