Giải phương trình log (log x)+log(log {x^3}-2) = 0

\(\begin{array}{l} \log (\log x) + \log (\log {x^3} - 2) = 0 \Leftrightarrow \left\{ {\begin{array}{*{20}{c}} \begin{array}{l} \log {x^3} - 2 > 0\\ \log x > 0 \end{array}\\ {\log x.(\log {x^3} - 2) = 1} \end{array}} \right.\\ \Leftrightarrow \left\{ {\begin{array}{*{20}{c}} \begin{array}{l} \log {x^3} > 2\\ x > 1 \end{array}\\ {3{{(\log x)}^2} - 2\log x - 1 = 0} \end{array}} \right. \end{array}\)

\(\begin{array}{l} \Leftrightarrow \left\{ \begin{array}{l} x > \sqrt[3]{{100}}\\ (\log x - 1)(3\log x + 1) = 0 \end{array} \right. \Leftrightarrow \left[ \begin{array}{l} \log x = 1\\ \log x = - \frac{1}{3} < 0\,\,(Loai) \end{array} \right.\\ \Leftrightarrow \log x = 1 \Leftrightarrow x = 10. \end{array}\)