If x and y are irrational

2d3vljtq 2022-07-12 Answered
If x and y are irrational numbers then x to the power of y is irrational I am asked to prove or disprove this statement.
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Answers (1)

Zackery Harvey
Answered 2022-07-13 Author has 21 answers
An elementary solution: x = log 2 3 is irrational (otherwise if it equals m / n for positive integers m and n, 2 m = 3 n contradicting unique prime factorization). Now 2 is irrational and ( 2 ) 2 x = 3 is a counter-example.
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