Google
Câu hỏi: Cho hai số dương ${a, b}$, ${a \ne 1}$, thỏa mãn ${{\log _{{a^2}}}b + {\log _a}{b^2} = 2}$. Tính ${{\log _a}b}$.
A. ${2}$.
B. ${\dfrac{4}{5}}$.
C. ${\dfrac{8}{5}}$.
D. ${4}$.
A. ${2}$.
B. ${\dfrac{4}{5}}$.
C. ${\dfrac{8}{5}}$.
D. ${4}$.
Ta có
${{\log }_{{{a}^{2}}}}b+{{\log }_{a}}{{b}^{2}}=2\Leftrightarrow \dfrac{1}{2}{{\log }_{a}}b+2{{\log }_{a}}b=2$ $\Leftrightarrow \dfrac{5}{2}{{\log }_{a}}b=2\Leftrightarrow {{\log }_{a}}b=\dfrac{4}{5}$
${{\log }_{{{a}^{2}}}}b+{{\log }_{a}}{{b}^{2}}=2\Leftrightarrow \dfrac{1}{2}{{\log }_{a}}b+2{{\log }_{a}}b=2$ $\Leftrightarrow \dfrac{5}{2}{{\log }_{a}}b=2\Leftrightarrow {{\log }_{a}}b=\dfrac{4}{5}$
Đáp án B.