Phương trình \(\log _3^2x - 2{\log _{\frac{1}{3}}}...

B

- Hướng dẫn giải

\(\begin{array}{l}
\log _3^2x - 2{\log _{\sqrt 3 }}x - 2{\log _{\frac{1}{3}}}x - 3 = 0\,\,\left( {x > 0} \right)\\
 \Leftrightarrow \log _3^2x - 2.2.{\log _3}x - 2.\left( { - 1} \right){\log _3}x - 3 = 0\\
 \Leftrightarrow \log _3^2x - 2{\log _3}x - 3 = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
{\log _3}x = 3\\
{\log _3}x =  - 1
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = 27 = {x_2}\\
x = \frac{1}{3} = {x_1}
\end{array} \right.\left( {tm} \right)\\
 \Rightarrow P = {\log _3}{x_1} + {\log _{27}}{x_2} = {\log _3}\frac{1}{3} + {\log _{27}}27 =  - 1 + 1 = 0
\end{array}\)