Biết rằng \({\log _3}2 = a;{\log _3}5 = b;{\log _3...

D

- Hướng dẫn giải

Phương pháp giải:

Giải chi tiết:

\(\begin{array}{l}{\log _3}2 = a;{\log _3}5 = b;{\log _3}7 = c\\M = {\log _{140}}63 = {\log _{140}}\left( {{{7.3}^2}} \right) = {\log _{140}}7 + 2{\log _{140}}3 = \\= \frac{1}{{{{\log }_7}140}} + \frac{2}{{{{\log }_3}140}} = \frac{1}{{{{\log }_7}\left( {{2^2}.5.7} \right)}} + \frac{2}{{{{\log }_3}\left( {{2^2}.5.7} \right)}}\\= \frac{1}{{2{{\log }_7}2 + {{\log }_7}5 + 1}} + \frac{2}{{2{{\log }_3}2 + {{\log }_3}5 + {{\log }_3}7}}\\{\log _7}2 = \frac{{{{\log }_3}2}}{{{{\log }_3}7}} = \frac{{{{\log }_3}2}}{{{{\log }_3}5.{{\log }_5}7}} = \frac{a}{{bc}};\,\,{\log _7}5 = \frac{1}{c};\,\,{\log _3}7 = {\log _3}5.{\log _5}7 = bc\\\Rightarrow M = \frac{1}{{\frac{{2a}}{{bc}} + \frac{1}{c} + 1}} + \frac{2}{{2a + b + bc}} = \frac{{bc + 2}}{{2a + b + bc}}\end{array}\)

Chọn đáp án D.