# Infinite Recursive Logarithm Sequence

Calculus Level 1

A recursive sequence is defined as $$a_0=\pi$$ and $$a_n=\log_{a_{n-1}}{27}.$$

Given that $$\displaystyle\lim_{n\to\infty}{a_n}$$ exists, what is $$\displaystyle\lim_{n\to\infty}{a_n}?$$

Bonus: For what values of $$a_0$$ does $$\displaystyle\lim_{n\to\infty}{a_n}$$ exist?

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