Bob, are you sure about
\(x = \sqrt{2}\)
I believe we can use such a logic only if the sequence has a limit.
In other case if I use the same logic to equation:
\(a=x^{x^{\ldots}}=4\)
I will get:
\(ln(x^{x^{\ldots}}) = ln4\)
\(x^{x^{\ldots}}lnx = ln4\)
\(a lnx = ln4\)
\(4lnx =...
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