# 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.

Compare with this.

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