Don't be fooled!

Calculus Level 4

\[\huge a^{a^{a^{\cdot^{\cdot^\cdot}}}}=4\]

How many positive real solutions \(a\) does the above equation have?

Clarification: The value of the infinite power tower \(a^{a^{a^{.^{.^.}}}}\) is defined as the limit of the sequence \(x_0=a, x_{n+1}=a^{x_n}.\)

Bonus: Illustrate your solution with a Cobweb Plot.

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