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Câu hỏi: Cho $a>0$ và $a\ne 1$, khi đó ${{\log }_{a}}\sqrt{a\sqrt[3]{a}}$ bằng
A. $\dfrac{4}{3}.$
B. $\dfrac{5}{6}.$
C. $\dfrac{5}{3}.$
D. $\dfrac{2}{3}.$
A. $\dfrac{4}{3}.$
B. $\dfrac{5}{6}.$
C. $\dfrac{5}{3}.$
D. $\dfrac{2}{3}.$
Ta có: ${{\log }_{a}}\sqrt{a\sqrt[3]{a}}={{\log }_{a}}\sqrt{a.{{a}^{\dfrac{1}{3}}}}={{\log }_{a}}\sqrt{{{a}^{\dfrac{4}{3}}}}={{\log }_{a}}{{a}^{\dfrac{2}{3}}}=\dfrac{2}{3}.$
Đáp án D.