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....
