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Question Number 191966 by Shlock last updated on 04/May/23

Answered by mr W last updated on 04/May/23

y=x^x^(...) =x^y y=e^(yln x) (−yln x)e^(−yln x) =−ln x −y ln x=W(−ln x) y=−((W(−ln x))/(ln x)) −ln x≥−(1/e) ln x≤(1/e) ⇒0<x≤(e)^(1/e) ≈1.444668

y=xx...=xyy=eylnx(−ylnx)e−ylnx=−lnx−ylnx=W(−lnx)y=−W(−lnx)lnx−lnx⩾−1elnx⩽1e⇒0<x⩽ee≈1.444668

Commented by Shlock last updated on 04/May/23

Nice solution, sir!

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