Hi all,

A friend asked me if i could sove Ln(x)=-x in exact form.

The solution i gave was x=e^(-e)^(-e)^(-e)^...

Ln(x)=Ln[e^(-e)^(-e)^...]=(-e)^(-e)^(-e)^...=-x

Whilst exploring this answer i have had difficulty believing this to be well defined or even correct.

A similar problem is x^x^x^x....=2 (or 4)

Which can be solved as x^2=2 x=root 2

or x^4=4 x=root 2 also

I would apreciate any thoughts on this and infinite exponention. All proofs are welcome.