Biết \({\log _a}b = 3;\,\,\,{\log _a}c =  - 2\), t...

B

- Hướng dẫn giải

Phương pháp giải:

Giải chi tiết:

\(\begin{array}{l}\,\,\,\,{\log _a}\dfrac{{{a^2}\sqrt[4]{b}{c^2}}}{{\sqrt[3]{a}{b^4}\sqrt c }} = {\log _a}\left( {\dfrac{{{a^2}}}{{\sqrt[3]{a}}}.\dfrac{{\sqrt[4]{b}}}{{{b^4}}}.\dfrac{{{c^2}}}{{\sqrt c }}} \right)\\ = {\log _a}\left( {{a^{2 - \frac{1}{3}}}.{b^{\frac{1}{4} - 4}}.{c^{2 - \frac{1}{2}}}} \right) = {\log _a}\left( {{a^{\frac{5}{3}}}.{b^{ - \frac{{15}}{4}}}.{c^{\frac{3}{2}}}} \right)\\ = {\log _a}{a^{\frac{5}{3}}} + {\log _a}{b^{ - \frac{{15}}{4}}} + {\log _a}{c^{\frac{3}{2}}} = \dfrac{5}{3} - \dfrac{{15}}{4}{\log _a}b + \dfrac{3}{2}{\log _a}c\\ = \dfrac{5}{3} - \dfrac{{15}}{4}.3 + \dfrac{3}{2}.\left( { - 2} \right) =  - \dfrac{{151}}{{12}}.\end{array}\)

Chọn B.