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C

- Hướng dẫn giải

Đáp án C

Từ $3^x=4^x={12}^{-x}\left\{\begin{array}{l}x={\log }_{3}a\\ y={\log }_{4}a\\ z=-{\log }_{12}a\end{array}\right.\Rightarrow P={\log }_{3}a{\log }_{4}a-{\log }_{4}a{\log }_{12}a-{\log }_{12}a{\log }_{3}a$

$$\begin{gathered} \frac{1}{{\log }_{a}3{\log }_{a}4}-\frac{1}{{\log }_{a}4{\log }_{a}12}-\frac{1}{{\log }_{a}12{\log }_{a}3} \\ =\frac{{\log }_{a}12-{\log }_{a}3-{\log }_{a}4}{{\log }_{a}3{\log }_{a}4{\log }_{a}12}=\frac{{\log }_{a}1}{{\log }_{a}3{\log }_{a}4{\log }_{a}12}=0 \end{gathered}$$