Can an irrational number raised to an irrational power be

oliviayychengwh

oliviayychengwh

Answered question

2022-01-06

Can an irrational number raised to an irrational power be rational?
If it can be rational, how can one prove it?

Answer & Explanation

Ella Williams

Ella Williams

Beginner2022-01-07Added 28 answers

There is a classic example here. Consider A=22. Then A is either rational or irrational. If it is irrational, then we have A2=22=2
Juan Spiller

Juan Spiller

Beginner2022-01-08Added 38 answers

Consider, for example, 21π=x where x should probably be irrational but xπ=2
More generally, 2 and π can be replaced by other rational and irrational numbers, respectively.
Vasquez

Vasquez

Expert2022-01-11Added 669 answers

For example:
22log23=3

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