题目内容
设函数
【答案】分析:不等式f(x)>(x-1)lg4化简为1+2x+4xa>4x.将a分离得出a>
只须a大于g(x)=
的最小值即可.
解答:解:
=lg(1+2x+4xa)-lg4.
等式f(x)>(x-1)lg4即为
lg(1+2x+4xa)>xlg4=lg4x.
1+2x+4xa>4x.
将a分离得出a>
令g(x)=
=1-
,只须a大于g(x)的最小值即可
易知g(x)在[1,3]上单调递增,最小值为g(1)=1-
-
=
所以a>
故答案为:a>
点评:本题考查函数与不等式的综合.参数分离的思想方法.本题得出a大于g(x)=
的最小值是关键.


解答:解:

等式f(x)>(x-1)lg4即为
lg(1+2x+4xa)>xlg4=lg4x.
1+2x+4xa>4x.
将a分离得出a>

令g(x)=



易知g(x)在[1,3]上单调递增,最小值为g(1)=1-



所以a>

故答案为:a>

点评:本题考查函数与不等式的综合.参数分离的思想方法.本题得出a大于g(x)=


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