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I know this isn't stirctly math related but how do a I put \({x}^{{x}^{{x}^{x}}}\) goign on forever in wolfram alpha? I haven't been able to find an answer to this online.

 

I wanted to find out \({x}^{{x}^{{x}^{x}}}=2\) but I can't do it

 

Edit: I think the answer is \(\sqrt{2}\) but I'm not sure. I want to know how to do infinite exponents regardless.

 Jan 29, 2019
edited by Guest  Jan 29, 2019
 #1
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 Using  the log property that

x^x   =   a

 

x ln (x) = ln (a)

 

x =  ln (a) / ln (x)      repetitively

 

     

                  x

            x

       x

  x            =      2

 

 

    x

  x

x      ln(x)    =   ln (2)

 

 

      x

   x

x      =    [ ln 2] / [ ln x]

 

 

  x

x     ln (x)  =  ln ( ln(2) / [ ln x] )

 

   x

x      =    ln ( ln(2) / [ ln x] ) / [ ln x ]

 

 

x ln (x) =  ln (   ln ( ln(2) / [ ln x] ) / [ ln x ] )

 

x = ln (   ln ( ln(2) / [ ln x] ) / [ ln x ] ) / ln (x) 

 

This would...of course.....not be easy to evalute algebraically.....but....

 

WolframAlpha shows the solution ≈ 1.4466014....

 

 

cool cool cool          

 

 Jan 30, 2019
edited by CPhill  Jan 30, 2019

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