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Câu hỏi: Với các số dương a, b bất kì. Mệnh đề nào dưới đây đúng?
A. ${{\log }_{3}}\left( \dfrac{3{{a}^{2}}}{b} \right)=1+2{{\log }_{3}}a+{{\log }_{3}}b$
B. ${{\log }_{3}}\left( \dfrac{3{{a}^{2}}}{b} \right)=1+\dfrac{1}{2}{{\log }_{3}}a-{{\log }_{3}}b$
C. ${{\log }_{3}}\left( \dfrac{3{{a}^{2}}}{b} \right)=1+\dfrac{1}{2}{{\log }_{3}}a+{{\log }_{3}}b$
D. ${{\log }_{3}}\left( \dfrac{3{{a}^{2}}}{b} \right)=1+2{{\log }_{3}}a-{{\log }_{3}}b$
A. ${{\log }_{3}}\left( \dfrac{3{{a}^{2}}}{b} \right)=1+2{{\log }_{3}}a+{{\log }_{3}}b$
B. ${{\log }_{3}}\left( \dfrac{3{{a}^{2}}}{b} \right)=1+\dfrac{1}{2}{{\log }_{3}}a-{{\log }_{3}}b$
C. ${{\log }_{3}}\left( \dfrac{3{{a}^{2}}}{b} \right)=1+\dfrac{1}{2}{{\log }_{3}}a+{{\log }_{3}}b$
D. ${{\log }_{3}}\left( \dfrac{3{{a}^{2}}}{b} \right)=1+2{{\log }_{3}}a-{{\log }_{3}}b$
$\begin{aligned}
& {{\log }_{3}}\left( \dfrac{3{{a}^{2}}}{b} \right)={{\log }_{3}}\left( 3{{a}^{2}} \right)-{{\log }_{3}}b={{\log }_{3}}3+{{\log }_{3}}{{a}^{2}}-{{\log }_{3}}b \\
& \text{ =1+2}{{\log }_{3}}a-{{\log }_{3}}b \\
\end{aligned}$
& {{\log }_{3}}\left( \dfrac{3{{a}^{2}}}{b} \right)={{\log }_{3}}\left( 3{{a}^{2}} \right)-{{\log }_{3}}b={{\log }_{3}}3+{{\log }_{3}}{{a}^{2}}-{{\log }_{3}}b \\
& \text{ =1+2}{{\log }_{3}}a-{{\log }_{3}}b \\
\end{aligned}$
Đáp án D.