Question 66
Suppose a real number $x \gt 1$ satisfies
$$
\log_{2}\left(\log_{4} x\right) + \log_{4}\left(\log_{16} x\right) + \log_{16}\left(\log_{2} x\right) = 0
$$
Compute
$$
\log_{2}\left(\log_{16} x\right) + \log_{16}\left(\log_{4} x\right) + \log_{4}\left(\log_{2} x\right)
$$
$$
\log_{2}\left(\log_{4} x\right) + \log_{4}\left(\log_{16} x\right) + \log_{16}\left(\log_{2} x\right) = 0
$$
Compute
$$
\log_{2}\left(\log_{16} x\right) + \log_{16}\left(\log_{4} x\right) + \log_{4}\left(\log_{2} x\right)
$$