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Note that x = 5^(1/5) is not a solution to the infinite "power tower" equationx^x^x^x^x^... = 5(You'd think that the "5" in the exponent on the lefthandside can be recursively subtituted by x^x^x^5 _ad infinitum_ ; but no, that's not valid.)
From the thumbnail: Just from inspection, x = 5^(1/5) = ⁵√5 ≈ 1.3797296615 appears to be a solution. (Not sure if it's the only solution, though.)
Note that x = 5^(1/5) is not a solution to the infinite "power tower" equation
x^x^x^x^x^... = 5
(You'd think that the "5" in the exponent on the lefthandside can be recursively subtituted by x^x^x^5 _ad infinitum_ ; but no, that's not valid.)
From the thumbnail: Just from inspection, x = 5^(1/5) = ⁵√5 ≈ 1.3797296615 appears to be a solution. (Not sure if it's the only solution, though.)