Đáp án:
C
Giải thích các bước giải:
\(\begin{array}{l}
{\log _{({a^2}b)}}\left( {\frac{a}{{\sqrt {{b^3}} }}} \right)\\
= {\log _{({a^2}b)}}\left( {a.{b^{\frac{{ - 3}}{2}}}} \right)\\
= {\log _{({a^2}b)}}a + {\log _{({a^2}b)}}{b^{\frac{{ - 3}}{2}}}\\
= \frac{1}{{{{\log }_a}({a^2}b)}} - \frac{3}{2}.\frac{1}{{{{\log }_b}({a^2}b)}}\\
= \frac{1}{{{{\log }_a}{a^2} + {{\log }_a}b}} - \frac{3}{2}.\frac{1}{{{{\log }_b}{a^2} + {{\log }_b}b}}\\
= \frac{1}{{2 + \sqrt 3 }} - \frac{3}{2}.\frac{1}{{\frac{2}{{\sqrt 3 }} + 1}} = \frac{1}{{2 + \sqrt 3 }} - \frac{3}{2}.\frac{{\sqrt 3 }}{{2 + \sqrt 3 }} = \frac{{2 - 3\sqrt 3 }}{{4 + 2\sqrt 3 }}
\end{array}\)
