i know this is possible to find with iteration, but is it possible to find it algebraically?
This probably isn't what you mean by "algebraically" but if you take the logarithm of both sides of the equation you get ln(y)= xln(x) and then x= W(ln(y)) where W is the "Lambert W function" which is defined as the inverse function to xln(x).
... and the reason we talk about the Lambert W function is that none of the previously-defined standard functions would work.
so if x=y^y, then y=?
All you have done is swap x and y! If [itex]x= y^y[/itex] then, by the same formula I gave before, y= W(ln(x)).
what? i wasn't claiming to have done anything radical to the formula. all i wanted to know was what you do the w function of. but thank you for telling me
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