解不等式log2(x^2+6x+1)≤3.loga(x-2x)＞0（a＞0,a≠1）.

题目

解不等式log2(x^2+6x+1)≤3.loga(x-2x)＞0（a＞0,a≠1）.
要有详细过程（log后面的2,a是底数）

答案

log2(x^2+6x+1)≤3
=> log2(x^2+6x+1)≤log2(8)
=> x^2+6x+1≤8
=> -7≤x≤1
0loga(x-2/x)＞0
=> loga(x-2/x)＞loga(1)
=> (x-2/x)<1
=> -1a>1时
loga(x-2/x)＞0
=> loga(x-2/x)＞loga(1)
=> (x-2/x)>1
=> x<-1或x>2