解不等式log1/2(3-x)>=log2(x+3)-1

题目

解不等式log1/2(3-x)>=log2(x+3)-1

答案

log1/2 (3-x)≥log2 (x+3)-1-log2 (3-x)≥log2 (x+3)-log2 2log2 (3-x)+log2 (x+3)-log2 2≤0log2 [(3-x)(x+3)/2]≤log2 1因为2＞1,所以log2 x为增函数0＜(3-x)(x+3)/2≤10＜9-x²≤27≤x²＜9√7≤x＜3或-3...