Is it known whether $\log 2\pi$ is rational (where the base of the logarithm is $e$)? Or algebraic?
2026-03-25 07:39:50.1774424390
Is $\log 2\pi$ rational?
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You're trying to see if $(2\pi)^q=e^p$ for some $p,q\in\Bbb Z$, in particular this means $e,\pi$ are not algebraically independent (over $\Bbb Q$). This is not known to the date.