Giải bài 102 -105 trang 133 SGK giải tích nâng cao 12

102. $3{{\log }_{0,1}}{{10}^{2,4}}=-7,2{{\log }_{10}}10=-7,2$

Chọn (C)

103. $\left( 0,5 \right){{\log }_{2}}25+{{\log }_{2}}\left( 1,6 \right)={{\log }_{2}}5+{{\log }_{2}}\left( 1,6 \right)$

$={{\log }_{2}}\left( 5.1,6 \right)={{\log }_{2}}8=3$

Chọn (C)

104. $\dfrac{{{\log }_{2}}240}{{{\log }_{3,75}}2}-\dfrac{{{\log }_{2}}15}{{{\log }_{60}}2}+{{\log }_{2}}1$

$={{\log }_{2}}\left( 16.15 \right).{{\log }_{2}}\dfrac{15}{4}-{{\log }_{2}}15.{{\log }_{2}}\left( 15.4 \right)+0 \\ =\left( {{\log }_{2}}15+4 \right)\left( {{\log }_{2}}15-2 \right)-{{\log }_{2}}15\left( {{\log }_{2}}15+2 \right) \\ =\log _{2}^{2}15+2{{\log }_{2}}15-8-\log _{2}^{2}15-2{{\log }_{2}}15 \\ =-8$

Chọn (D)

105. ${{\left( \dfrac{3}{5} \right)}^{2x-1}}\le {{\left( \dfrac{3}{5} \right)}^{2-x}}$

$\Leftrightarrow 2x-1\ge 2-x \\ \Leftrightarrow 3x\ge 3 \\ \Leftrightarrow x\ge 1 \\ \Rightarrow S=\left[ 1;+\infty \right)$

Chọn (C)