Cho \({\log _{27}}\left| a \right| + {\log _9}{b^2} = 5\) và \({\log _{27}}\left| b \right| + {\log _9}{a^2} = 7\).

* Hướng dẫn giải

\(\left\{ \begin{array}{l}
\frac{1}{3}{\log _3}\left| a \right| + {\log _3}\left| b \right| = 5\\
{\log _3}\left| a \right| + \frac{1}{3}{\log _3}\left| b \right| = 7
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
{\log _3}\left| a \right| = 6\\
{\log _3}\left| b \right| = 3
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
\left| a \right| = 729\\
\left| b \right| = 27
\end{array} \right..\)