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Why is ln($\pi^{\pi}$) rational?

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closed as off topic by darij grinberg, Ryan Budney, Henry Cohn, Yemon Choi, Tom Church Feb 19 '12 at 0:53

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It is not known if it is rational. It's suspected to be transcendental over $\mathbb Q$. It is known that $e^\pi$ is transcendental, but none of $e^e,\pi^e,\pi^\pi$ is known to be irrational or transcendental.

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