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From: ron@brl-tgr.ARPA (Ron Natalie <ron>)
Newsgroups: net.puzzle
Subject: Re: x to the x to the x ...
Message-ID: <10214@brl-tgr.ARPA>
Date: Thu, 25-Apr-85 20:47:26 EST
Article-I.D.: brl-tgr.10214
Posted: Thu Apr 25 20:47:26 1985
Date-Received: Sat, 27-Apr-85 05:42:07 EST
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> > 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?
> > 
> 
> let y = x^x^x^...   then y = x^y.
> y=2, now take log of both sides , ln y = ln2  or ln (x^y) =ln 2.
> but ln(x^y) = y*ln x  and y=2. so we have 2*ln x =ln 2. Or if I can do this
> right x= 2-e^2. Is this right?
> 
Close

	2 * ln x = ln 2		You have this right
	    ln x = .5 ln 2
	       x = 2^.5 or sqrt of 2

You can't do division by subtraction unless you take another log.

-Ron