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Câu hỏi: Cho $a>0$ thỏa mãn $\ln a=\dfrac{4}{3}$. Tính $\ln \left( {{e}^{3}}.\sqrt{a} \right)$.
A. $\dfrac{14}{3}$.
B. $\dfrac{11}{3}$.
C. $\dfrac{3}{\sqrt{2}}$.
D. $\dfrac{3}{4}$.
A. $\dfrac{14}{3}$.
B. $\dfrac{11}{3}$.
C. $\dfrac{3}{\sqrt{2}}$.
D. $\dfrac{3}{4}$.
Ta có: $\ln \left( {{e}^{3}}.\sqrt{a} \right)=\ln \left( {{e}^{3}} \right)+\ln \left( {{a}^{\dfrac{1}{2}}} \right)=3+\dfrac{1}{2}\ln a=3+\dfrac{1}{2}.\dfrac{4}{3}=\dfrac{11}{3}.$.
Đáp án B.