# Logarithm Question

• Jan 28th 2009, 03:41 PM
s3a
Logarithm Question
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!
• Jan 28th 2009, 03:53 PM
Plato
$\begin{gathered}
\log _3 \left[ {\log _3 \left( {\log _3 \left[ {\log _3 (x)} \right]} \right)} \right] = 0 \hfill \\
\Rightarrow \log _3 \left( {\log _3 \left[ {\log _3 (x)} \right]} \right) = 1 \hfill \\
\Rightarrow \log _3 \left[ {\log _3 (x)} \right] = 3 \hfill \\
\Rightarrow \log _3 (x) = 27 \hfill \\
\Rightarrow x = ? \hfill \\
\end{gathered}$