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Math Help - Logarithm Question

  1. #1
    s3a
    s3a is offline
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    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!
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  2. #2
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    \begin{gathered}<br />
  \log _3 \left[ {\log _3 \left( {\log _3 \left[ {\log _3 (x)} \right]} \right)} \right] = 0 \hfill \\<br />
   \Rightarrow \log _3 \left( {\log _3 \left[ {\log _3 (x)} \right]} \right) = 1 \hfill \\<br />
   \Rightarrow \log _3 \left[ {\log _3 (x)} \right] = 3 \hfill \\<br />
   \Rightarrow \log _3 (x) = 27 \hfill \\<br />
   \Rightarrow x = ? \hfill \\ <br />
\end{gathered}
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