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Câu hỏi: Cho a, b > 0 thõa mãn $\dfrac{{{\log }_{3}}5.{{\log }_{5}}a}{1+{{\log }_{3}}2}-{{\log }_{6}}b=2$. Tìm khẳng định đúng?
A. $a=b{{\log }_{6}}2$
B. $a=b{{\log }_{6}}3$
C. $a=36b$
D. $2a+3b=0$
A. $a=b{{\log }_{6}}2$
B. $a=b{{\log }_{6}}3$
C. $a=36b$
D. $2a+3b=0$
Ta có $\dfrac{{{\log }_{3}}a}{{{\log }_{3}}6}-{{\log }_{6}}b=2\Leftrightarrow {{\log }_{3}}a-{{\log }_{3}}6.{{\log }_{6}}b=2{{\log }_{3}}6$
$\Leftrightarrow {{\log }_{3}}a-{{\log }_{3}}b={{\log }_{3}}36\Leftrightarrow {{\log }_{3}}\dfrac{a}{b}={{\log }_{3}}36\Leftrightarrow \dfrac{a}{b}=36$.
$\Leftrightarrow {{\log }_{3}}a-{{\log }_{3}}b={{\log }_{3}}36\Leftrightarrow {{\log }_{3}}\dfrac{a}{b}={{\log }_{3}}36\Leftrightarrow \dfrac{a}{b}=36$.
Đáp án C.