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Câu hỏi: Đặt ${{\log }_{2}}a=x,{{\log }_{2}}b=y$. Biết ${{\log }_{\sqrt{8}}}\sqrt[3]{a{{b}^{2}}}=m\text{x}+ny$. Tìm $T=m+n$.
A. $T=\dfrac{3}{2}$
B. $T=\dfrac{2}{3}$
C. $T=\dfrac{2}{9}$
D. $T=\dfrac{8}{9}$
A. $T=\dfrac{3}{2}$
B. $T=\dfrac{2}{3}$
C. $T=\dfrac{2}{9}$
D. $T=\dfrac{8}{9}$
${{\log }_{{{2}^{\dfrac{3}{2}}}}}{{(a{{b}^{2}})}^{\dfrac{1}{3}}}=\dfrac{1}{3}.\dfrac{3}{2}{{\log }_{2}}(a{{b}^{2}})=\dfrac{2}{9}({{\log }_{2}}a+2{{\log }_{2}}b)\Rightarrow m=\dfrac{2}{9};n=\dfrac{4}{9}\Rightarrow m+n=\dfrac{2}{3}$.
Đáp án B.