Tagged Questions

12
votes
1answer
151 views

Is the positive root of the equation $x^{x^x}=2$, $x=1.47668433…$ a transcendental number?

I can prove using the Gelfond–Schneider theorem that the positive root of the equation $x^{x^x}=2$, $x=1.47668433...$ is an irrational number. Is it possible to prove it is transcendental?
5
votes
0answers
290 views

Is ${^5\pi}$ an integer? [duplicate]

Possible Duplicate: How to show $e^{e^{e^{79}}}$ is not an integer Is ${^5\pi}$ an integer? It is "obviously" not, right? But can we prove it? Here ${^5\pi}$ means the result of tetration ...