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Câu hỏi: Dặt $a={{\log }_{2}}5$ và $b={{\log }_{3}}5$. Biểu diễn đúng ${{\log }_{6}}5$ theo a, b là:
A. $\dfrac{1}{a+b}.$
B. $a+b.$
C. $\dfrac{ab}{a+b}.$
D. $\dfrac{a+b}{ab}.$
A. $\dfrac{1}{a+b}.$
B. $a+b.$
C. $\dfrac{ab}{a+b}.$
D. $\dfrac{a+b}{ab}.$
Ta có: ${{\log }_{5}}2=\dfrac{1}{{{\log }_{2}}5}=\dfrac{1}{a};{{\log }_{5}}3=\dfrac{1}{{{\log }_{3}}5}=\dfrac{1}{b}$
${{\log }_{6}}5=\dfrac{1}{{{\log }_{5}}6}=\dfrac{1}{{{\log }_{5}}2+{{\log }_{5}}3}=\dfrac{1}{\dfrac{1}{a}+\dfrac{1}{b}}=\dfrac{ab}{a+b}$
${{\log }_{6}}5=\dfrac{1}{{{\log }_{5}}6}=\dfrac{1}{{{\log }_{5}}2+{{\log }_{5}}3}=\dfrac{1}{\dfrac{1}{a}+\dfrac{1}{b}}=\dfrac{ab}{a+b}$
Đáp án C.