(7)已知 $a=\log _{2} 3+\log _{2} \sqrt{3}, b=\log _{2} 9-\log _{2} \sqrt{3}, c=\log _{3} 2$ 则 $\mathrm{a}, \mathrm{b}, \mathrm{c}$ 的大小关系是
参考答案:$B$
2012_退役省自主命题 (2012·文)
(7)已知 $a=\log _{2} 3+\log _{2} \sqrt{3}, b=\log _{2} 9-\log _{2} \sqrt{3}, c=\log _{3} 2$ 则 $\mathrm{a}, \mathrm{b}, \mathrm{c}$ 的大小关系是
【答案】:$B$
【解析】:$a=\log _{2} 3+\log _{2} \sqrt{3}=\log _{2} 3+\frac{1}{2} \log _{2} 3=\frac{3}{2} \log _{2} 3$ ,
$b=\log _{2} 9-\log _{2} \sqrt{3}=2 \log _{2} 3-\frac{1}{2} \log _{2} 3=\frac{3}{2} \log _{2} 3, c=\log _{3} 2=\frac{\log _{2} 2}{\log _{2} 3}=\frac{1}{\log _{2} 3}$ 则
$a=b>c$
【考点定位】本题考查对数函数运算.