Cho \(a = {\log _2}3,b = {\log _3}5,c = {\log _7}2\). Tính \({\log _{140}}63\) theo \(a, b, c\)

* Hướng dẫn giải

Ta có \({\log _{140}}63 = \frac{{{{\log }_7}63}}{{{{\log }_7}140}} = \frac{{1 + 2{{\log }_7}3}}{{1 + 2{{\log }_7}2 + {{\log }_7}5}} = \frac{{1 + 2{{\log }_7}2.{{\log }_2}3}}{{1 + 2{{\log }_7}2 + {{\log }_7}2.{{\log }_2}3.{{\log }_3}5}}\)