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How do you approach a problem like (solve for $x$):

$x^{x^{x^{x^{...}}}}=2$

Also, I have no idea what to tag this as.

Thanks for any help.

1 Answers 1

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I'm just going to give you a HUGE hint. and you'll get it right way. Let $f(x)$ be the left hand expression. Clearly, we have that the left hand side is equal to $x^{f(x)}$. Now, see what you can do with it.

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    Correcting my earlier comment: It does not fail when the righthand side is $4$. The restriction on $x$, however, is correct.2012-07-04