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Câu hỏi: Cho $0<a\ne 1$. Giá trị của biểu thức $P={{\log }_{a}}\left( a.\sqrt[3]{{{a}^{2}}} \right)$ là:
A. $\dfrac{4}{3}$.
B. $3$.
C. $\dfrac{5}{3}$.
D. $\dfrac{5}{2}$.
Ta có: $P={{\log }_{a}}\left( a.\sqrt[3]{{{a}^{2}}} \right)$ $={{\log }_{a}}\left( a.{{a}^{\dfrac{2}{3}}} \right)$ $={{\log }_{a}}{{a}^{\dfrac{5}{3}}}$ $=\dfrac{5}{3}$.
A. $\dfrac{4}{3}$.
B. $3$.
C. $\dfrac{5}{3}$.
D. $\dfrac{5}{2}$.
Ta có: $P={{\log }_{a}}\left( a.\sqrt[3]{{{a}^{2}}} \right)$ $={{\log }_{a}}\left( a.{{a}^{\dfrac{2}{3}}} \right)$ $={{\log }_{a}}{{a}^{\dfrac{5}{3}}}$ $=\dfrac{5}{3}$.
Đáp án C.