Is a an integer to the power of an irrational

Erin Lozano

Erin Lozano

Answered question

2022-06-14

Is a an integer to the power of an irrational number irrational?

Answer & Explanation

scoseBexgofvc

scoseBexgofvc

Beginner2022-06-15Added 20 answers

Let 3 = 2 l o g 23. We show that log 2 3 is indeed irrational; if 2 m n = 3 for some integers n , m 1 then raising both sides to the n-th power gives 2 m = 3 n for some integers m , n. Which is impossible as 2 m is even and 3 n is odd.

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