Question

已知-3≤log以1/2为底x的对数≤-1/2,求函数y=(log2为底 x/2的对数)(log2为底 x/4的对数)的

Answer 1

-3=log(1/2)8,-1/2=log(1/2)√2

因为0＜1/2＜1,因此为减函数,√2≤x≤8

y=(log2 x-log2 2)(log2 x-log2 4)

=(log2 x -1)(log2 x -2)

√2≤x≤8,1/2≤log2 x≤3

设log2 x=t

y=t²-3t+2

=(t-3/2)²-1/4

1/2≤t≤3

当t=3/2时有最小值-1/4；当t=3时,有最大值2

值域为〔-1/4,2〕