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Câu hỏi: Đặt $a={{\log }_{5}}2$, khi đó ${{\log }_{16}}\left( \ln {{e}^{125}} \right)$ bằng
A. $\dfrac{3a}{4}$
B. $\dfrac{3}{4a}$
C. $\dfrac{4}{3a}$
D. $\dfrac{4a}{3}$
A. $\dfrac{3a}{4}$
B. $\dfrac{3}{4a}$
C. $\dfrac{4}{3a}$
D. $\dfrac{4a}{3}$
Ta có: ${{\log }_{16}}\left( \ln {{e}^{125}} \right)={{\log }_{16}}125=\dfrac{3}{4}{{\log }_{2}}5=\dfrac{3}{4}.\dfrac{1}{{{\log }_{5}}2}=\dfrac{3}{4a}$
Đáp án B.