Đặt  \(a = {\log _2}3,b = {\log _5}3\...

C

- Hướng dẫn giải

\({\log _6}45 = \frac{{{{\log }_2}45}}{{{{\log }_2}6}} = \frac{{{{\log }_2}\left( {5.9} \right)}}{{{{\log }_2}\left( {2.3} \right)}} = \frac{{{{\log }_2}5 + 2{{\log }_2}3}}{{1 + {{\log }_2}3}}\)

\(= \frac{{{{\log }_2}3.{{\log }_3}5 + 2{{\log }_2}3}}{{1 + {{\log }_2}3}} = \frac{{{{\log }_2}3.\frac{1}{{{{\log }_3}5}} + 2.{{\log }_2}3}}{{1 + {{\log }_2}3}}\)

\(= \frac{{\frac{a}{b} + 2{\rm{a}}}}{{1 + a}} = \frac{{a + 2ab}}{{ab + b}}\)