求函数y=log2(x/4)×log4(x/2)(2≤x≤4)的值域
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![求函数y=log2(x/4)×log4(x/2)(2≤x≤4)的值域](/uploads/image/z/1064375-71-5.jpg?t=%E6%B1%82%E5%87%BD%E6%95%B0y%3Dlog2%EF%BC%88x%2F4%EF%BC%89%C3%97log4%EF%BC%88x%2F2%EF%BC%89%282%E2%89%A4x%E2%89%A44%29%E7%9A%84%E5%80%BC%E5%9F%9F)
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求函数y=log2(x/4)×log4(x/2)(2≤x≤4)的值域
求函数y=log2(x/4)×log4(x/2)(2≤x≤4)的值域
求函数y=log2(x/4)×log4(x/2)(2≤x≤4)的值域
y=log2(x/4)×log4(x/2)
=[log2(x)-2]*[0.5log2(x)-0.5]
=0.5[log2(x)]²-1.5log2(x)+1
=0.5[log2(x)-1.5]²-0.125
2≤x≤4
1≤log2(x)≤2
0≤[log2(x)-1.5]²≤0.25
-0.125≤y≤0
函数y=log2(x/4)×log4(x/2)(2≤x≤4)的值域是[-0.125,0]
log2(3/2)<=y<=log2(5)