Học lớp hướng dẫn giải
Điều kiện: \(\left\{ \begin{array}{l} x > 0\\ {\log _2}x > 0\\ {\log _4}x > 0 \end{array} \right. \Leftrightarrow x > 1.\)
\(\begin{array}{l} {\log _4}({\log _2}x) + {\log _2}({\log _4}x) = 2\\ \Leftrightarrow \frac{1}{2}{\log _2}({\log _2}x) + {\log _2}\left( {\frac{1}{2}{{\log }_2}x} \right) = 2\\ \Leftrightarrow \frac{1}{2}{\log _2}({\log _2}x) + {\log _2}({\log _2}x) - 1 = 2\\ \Leftrightarrow {\log _2}({\log _2}x) = 2 \Leftrightarrow {\log _2}x = 4 \Leftrightarrow x = 16 \end{array}\)