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Calculus Level 4

What can we say about positive real solutions to the equations

$\Large x^{{x}^{2018}} = 2018\quad \text{ and }\quad x^{x^{x^{^ {.^{.^.} } } }} = 2018\,?$

One exists, the other does not They exist, and are the same They exist, but are different

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by Calvin Lin

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