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From: smp@gitpyr.UUCP (Scott M Pfeffer)
Newsgroups: net.puzzle
Subject: Re: x to the x to the x ... (ANSWER/SPOILER)
Message-ID: <351@gitpyr.UUCP>
Date: Thu, 25-Apr-85 20:13:28 EST
Article-I.D.: gitpyr.351
Posted: Thu Apr 25 20:13:28 1985
Date-Received: Sat, 27-Apr-85 04:49:56 EST
References: <748@whuxlm.UUCP>
Reply-To: smp@gitpyr.UUCP (Scott M Pfeffer)
Distribution: net
Organization: Georgia Institute of Technology
Lines: 48

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
>
>the x's go on forever and the carots mean "power of", not "exclusive OR".
>What is the value of x?
>
>By the way, I had to look up the answer the first time I saw this --
>Did anybody get it without cheating?
>
>Bill Stoll, ..!whuxlm!wws

    This problem is solved as follows:

    1.  x^x^x^ ... = 2    (given in original problem)


               x^x^x^ ...
    2.  log (x           ) = log (2)
           2                    2


    3.  (x^x^x ...) log (x) = 1
                       2 


    4.  2 log (x) = 1     (remember that (x^x^x^ ... = 2) )
             2


    5.  log (x) = 1/2
           2

             (1/2)
    6.  x = 2


    I think that this problem came from the 1984 test, but I am note sure.
    I also believe that the original problem asked not what (x^x^x^ ...) is
    but rather wanter the student to figure out what   1/2  1/2  1/2
                                                      2  ^ 2    ^    ...
 
    is equal to.  I may be wrong.
 
  
          Scott Pfeffer
          {agkua,hplabs}!gatech!gitpyr!smp