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?
2026-03-26 03:13:35.1774494815
Is the positive root of the equation $x^{x^x}=2$, $x=1.47668433...$ a transcendental number?
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I believe, it is a known open problem. Ditto for ${^3 x}=3$, ${^3 x}=4$, ${^3 x}=5$ (left superscript denotes tetration).