已知2(log以1/2为底x)²+7log以1/2为底x+3≤0,求函数y=(log以2为底x/2)乘以(log以1/2为底4/x)的最大值和最小值,
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![已知2(log以1/2为底x)²+7log以1/2为底x+3≤0,求函数y=(log以2为底x/2)乘以(log以1/2为底4/x)的最大值和最小值,](/uploads/image/z/14975140-4-0.jpg?t=%E5%B7%B2%E7%9F%A52%EF%BC%88log%E4%BB%A51%2F2%E4%B8%BA%E5%BA%95x%29%26%23178%3B%2B7log%E4%BB%A51%2F2%E4%B8%BA%E5%BA%95x%2B3%E2%89%A40%2C%E6%B1%82%E5%87%BD%E6%95%B0y%3D%28log%E4%BB%A52%E4%B8%BA%E5%BA%95x%2F2%29%E4%B9%98%E4%BB%A5%28log%E4%BB%A51%2F2%E4%B8%BA%E5%BA%954%2Fx%29%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E5%92%8C%E6%9C%80%E5%B0%8F%E5%80%BC%2C)
已知2(log以1/2为底x)²+7log以1/2为底x+3≤0,求函数y=(log以2为底x/2)乘以(log以1/2为底4/x)的最大值和最小值,
已知2(log以1/2为底x)²+7log以1/2为底x+3≤0,求函数y=(log以2为底x/2)
乘以(log以1/2为底4/x)的最大值和最小值,
已知2(log以1/2为底x)²+7log以1/2为底x+3≤0,求函数y=(log以2为底x/2)乘以(log以1/2为底4/x)的最大值和最小值,
∵2(log以1/2为底x)²+7log以1/2为底x+3≤0
∴-3≤log1/2 x≤-1/2
∴1/2≤log2 x≤3
∴-0.5≤log2 x -1.5≤1.5
0≤(log2 x -1.5)²≤9/4
∵y=(log以2为底x/2)乘以(log以1/2为底4/x)
=(log2 x-1)(log2 x-2)
=(log2 x-1.5)²-1/4
∴-1/4≤y≤2
∴y的最大值2和最小值-1/4