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How to put infinite powers in wolfram alpha?

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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

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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....   Jan 30, 2019
edited by CPhill  Jan 30, 2019