解对数不等式log2 x>(log1/4 x)+3
问题描述：
解对数不等式
log2 x>(log1/4 x)+3
答
log2(x)＞log1/4(x)+3
log2(x)＞log2^-2(x)+3
log2（x)＞-1/2log2(x)+3
log2(x)+1/2log2(x)＞3
3/2log2(x)＞3
log2(x)＞2
∴x＞4
答
log2x-1/2log2x^-1>3
log2(x/(x^-1/2))>3
log2x^3/2>3
x^3/2>8
x>4
答
log1/4 x=lgx/lg(1/4)=lgx/lg2^(-2)=lgx/(-2lg2)=(-1/2)log2(x)
所以log2(x)>(-1/2)log2(x)+3
(3/2)log2(x)>3
log2(x)>2=log2(4)
底数2>1
所以log2(x)是增函数
所以x>4