Logarithm Question

**s3a** · January 28th 2009, 02:41 PM

Ok before my ask my question I'd like to say that log3 means log base 3 and log 3 means log base 10 of 3:

How do I solve the following?

log3 (log3 (log3 (log3 x))) = 0

Any help would be greatly appreciated!
Thanks!

**Plato** · January 28th 2009, 02:53 PM

$\begin{gathered} \log _3 \left[ {\log _3 \left( {\log _3 \left[ {\log _3 (x)} \right]} \right)} \right] = 0 \hfill \\ \Rightarrow \log _3 \left( {\log _3 \left[ {\log _3 (x)} \right]} \right) = 1 \hfill \\ \Rightarrow \log _3 \left[ {\log _3 (x)} \right] = 3 \hfill \\ \Rightarrow \log _3 (x) = 27 \hfill \\ \Rightarrow x = ? \hfill \\ \end{gathered}$

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