# More Fun With Power Towers

Calculus Level 4

$\huge a^{a^{a^{\cdot^{\cdot^\cdot}}}}=b$

Find the largest real number $$b$$ such that the above equation has a positive real solution $$a$$. Approximate $$b$$ to four significant digits.

If you come to the conclusion that no such value of $$b$$ exists, enter 666.

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

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