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From: js2j@mhuxt.UUCP (sonntag)
Newsgroups: net.puzzle
Subject: Re: x to the x to the x ... (ANSWER/SPOILER)
Message-ID: <821@mhuxt.UUCP>
Date: Mon, 29-Apr-85 15:10:44 EDT
Article-I.D.: mhuxt.821
Posted: Mon Apr 29 15:10:44 1985
Date-Received: Tue, 30-Apr-85 06:11:42 EDT
References: <748@whuxlm.UUCP> <351@gitpyr.UUCP>
Organization: AT&T Bell Laboratories, Murray Hill
Lines: 28

> In article <748@whuxlm.UUCP> wws@whuxlm.UUCP (Stoll W William) writes:
> >This one may be old, it's from an old MAA test.
> >
> >x^x^x^x... = 2
> >
>     This problem is solved as follows:
> 
    <solution deleted.  Presumably you've all seen it by now.>
I couldn't figure out exactly what was wrong with the derivation, but
Scott's answer:
>              (1/2)
>     6.  x = 2

     Is easily demonstrated to be wrong, with the help of my trusty TI-58.
Let x=2^(1/2).
          x^x=1.632...
	  x^x^x=2.000...
	  x^x^x^x=2.665..., and the series just keeps on growing.  I suspect
that the problem *has* no solution, and that x^x^x...=1 for  0<x<=1 and that
x^x^x^x...approaches infinity for x>1.
     I suppose that it is possible that there exists some non-real solution.
-- 
Jeff Sonntag
ihnp4!mhuxt!js2j
    "This here's a story 'bout Minnie the Moocher.
     She was a low-down hoo-oochy koocher.
     She was the roughest, meanest frail.
     But Minnie had a heart as big as a whale." - idunno (mail me if you do!)