Question

高一数学，大神求助！！！

已知x满足2（log2x）^2+7log2x+3小于等于0，求x的取值范围。要过程啊！！

Answer 1

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