赞 shaoyezhen 幼苗
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f(x) = log2 (x/2) *log2 (x/4)
= [ log2 (x) - log2 (2) ]*[ log2(x) - log2(4)]
= [ log2 (x) - 1 ] * [ log2 (x) - 2 ]
设 t = log2 (x)
√2 ≤ x ≤ 8
1/2 ≤ t ≤ 3
f(x) = (t-1)(t-2) = t² - 3t + 2
= (t - 3/2)² - 1/4
当 t = 3/2 时取最小值 -1/4
当 t=3 时取最大值 2
= [ log2 (x) - log2 (2) ]*[ log2(x) - log2(4)]
= [ log2 (x) - 1 ] * [ log2 (x) - 2 ]
设 t = log2 (x)
√2 ≤ x ≤ 8
1/2 ≤ t ≤ 3
f(x) = (t-1)(t-2) = t² - 3t + 2
= (t - 3/2)² - 1/4
当 t = 3/2 时取最小值 -1/4
当 t=3 时取最大值 2
1年前
9
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