Schanuel's Conjecture Implies Transcendence of Log Pi

Theorem
Let Schanuel's Conjecture be true.

Then the logarithm of $\pi$ (pi):
 * $\ln \pi$

is transcendental.

Proof
Assume the truth of Schanuel's Conjecture.

From Schanuel's Conjecture Implies Algebraic Independence of Pi and Log of Pi over the Rationals, $\ln \pi$ and $\pi$ are algebraically independent over the rational numbers $\Q$.

Therefore, if Schanuel's Conjecture holds, $\ln \pi$ must be transcendental.