Toán 12 Biểu diễn logarit \({\log _{60}}1050\) theo a, b, c.

Đặt \(a = {\log _2}3,b = {\log _2}5,c = {\log _2}7\). Biểu diễn \({\log _{60}}1050\) theo a, b, c.
A. \({\log _{60}}1050 = \frac{{1 + a + 2b + c}}{{1 + 2a + b}}\)
B. \({\log _{60}}1050 = \frac{{1 + a + 2b + c}}{{2 + a + b}}\)
C. \({\log _{60}}1050 = \frac{{1 + a + b + 2c}}{{1 + 2a + b}}\)
D. \({\log _{60}}1050 = \frac{{1 + 2a + b + c}}{{2 + a + b}}\)

\(\begin{array}{l} {\log _{60}}1050 = \frac{{{{\log }_2}1050}}{{{{\log }_2}60}} = \frac{{{{\log }_2}(2.5.5.3.7)}}{{{{\log }_2}(2.2.3.5)}}\\ = \frac{{1 + 2{{\log }_2}(5) + {{\log }_2}(3) + {{\log }_2}(7)}}{{2 + {{\log }_2}(3) + {{\log }_2}(5)}} = \frac{{1 + a + 2b + c}}{{2 + a + b}} \end{array}\)