1. Let $x>1$, if
$$
\log _{2}\left(\log _{4} x\right)+\log _{4}\left(\log _{16} x\right)+\log _{16}\left(\log _{2} x\right)=0 \text {, }
$$

then $\log _{2}\left(\log _{16} x\right)+\log _{16}\left(\log _{4} x\right)+\log _{4}\left(\log _{2} x\right)=$
$\qquad$
1. $-\frac{1}{4}$.
The desired expression minus the condition expression yields
$$
\begin{array}{l}
\log _{2}\left(\log _{16} 4\right)+\log _{4}\left(\log _{2} 16\right)+\log _{16}\left(\log _{4} 2\right) \\
=-\frac{1}{4} .
\end{array}
$$