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Câu hỏi: Cho $0<a\ne 1 ; b,c>0$ thỏa mãn ${{\log }_{a}}b=3 ; {{\log }_{a}}c=-2$. Tính ${{\log }_{a}}\left( {{a}^{3}}{{b}^{2}}\sqrt{c} \right)$.
A. $10$.
B. $8$.
C. $-18$.
D. $7$.
A. $10$.
B. $8$.
C. $-18$.
D. $7$.
$\begin{aligned}
& {{\log }_{a}}\left( {{a}^{3}}{{b}^{2}}\sqrt{c} \right)={{\log }_{a}}{{a}^{3}}+{{\log }_{a}}{{b}^{2}}+{{\log }_{a}}\sqrt{c} \\
& =3{{\log }_{a}}a+2{{\log }_{a}}b+\dfrac{1}{2}{{\log }_{a}}c=3+2.3+\dfrac{1}{2}.(-2)=8 \\
\end{aligned}$
& {{\log }_{a}}\left( {{a}^{3}}{{b}^{2}}\sqrt{c} \right)={{\log }_{a}}{{a}^{3}}+{{\log }_{a}}{{b}^{2}}+{{\log }_{a}}\sqrt{c} \\
& =3{{\log }_{a}}a+2{{\log }_{a}}b+\dfrac{1}{2}{{\log }_{a}}c=3+2.3+\dfrac{1}{2}.(-2)=8 \\
\end{aligned}$
Đáp án B.