Câu 104. Giá trị biểu thức \({{lo{g_2}240} \over {{{\log }_{3,75}}2}} - {{{{\log }_2}15} \over {{{\log }_{60}}2}} + {\log _2}1\) bằng:

(A) 4;                            (B) 3;

(C) 1;                            (D) – 8

Giải

\(\eqalign{
& {{lo{g_2}240} \over {{{\log }_{3,75}}2}} - {{{{\log }_2}15} \over {{{\log }_{60}}2}} + {\log _2}1 =  {lo{g_2}240}.{\log _2}3,75 - {\log _2}15.{\log _2}\left( {15.4} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {{{\log }_2}15 + 4} \right){\log _2}{{15} \over 4} - {\log _2}15\left( {{{\log }_2}15 + 2} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {{{\log }_2}15 + 4} \right)\left( {{{\log }_2}15 - 2} \right) - {\log _2}15\left( {{{\log }_2}15 + 2} \right) = - 8 \cr} \)

Chọn (D).