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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