已知x满足2（log2x）^2+7log2x+3小于等于0,求x的取值范围._数学解答

已知x满足2（log2x）^2+7log2x+3小于等于0,求x的取值范围.

人气：458 ℃　时间：2020-03-21 02:24:34

解答

设log2x=t
2t^2+7t+3≤0
(2t+1)(t+3)≤0
-3≤t≤-1/2
-log2 8≤log2 x≤-log2√2
log2 1/8≤log2 x≤-log2 √2/2
∵底数＞1
∴1/8≤x≤√2/2