Question 166
Suppose a real number $x \gt 1$ satisfies
$$
\log_{\sqrt[3]{3}}\left(\log_{3} x\right) + \log_{3}\left(\log_{27} x\right) + \log_{27}\left(\log_{\sqrt[3]{3}} x\right) = 1
$$
Compute $\log_{3}\left(\log_{3} x\right)$.
$$
\log_{\sqrt[3]{3}}\left(\log_{3} x\right) + \log_{3}\left(\log_{27} x\right) + \log_{27}\left(\log_{\sqrt[3]{3}} x\right) = 1
$$
Compute $\log_{3}\left(\log_{3} x\right)$.