\(\begin{array}{l} \log _2^2x - 2{\log _4}(4x) - 4 = 0 \Leftrightarrow \left\{ \begin{array}{l} x > 0\\ {\left( {{{\log }_2}x} \right)^2} - (2 - {\log _2}x) - 4 = 0 \end{array} \right.\\ \Leftrightarrow \left\{ \begin{array}{l} x > 0\\ {({\log _2}x)^2} - {\log _2}x - 6 = 0 \end{array} \right. \end{array}\)
\(\Leftrightarrow \left\{ \begin{array}{l} x > 0\\ ({\log _2}x - 3)({\log _2}x + 2) = 0 \end{array} \right. \Leftrightarrow \left[ {\begin{array}{*{20}{c}} {x = 8}\\ {x = \frac{1}{4}} \end{array}} \right. \Rightarrow {x_1}.{x_2} = 8.\frac{1}{4} = 2\)
