已知x满足不等式2[㏒(1/2)^x]²+7㏒(1/2)^x+3≤0,求函数f(x)={㏒[2^(x/4)]}*{㏒[2^(x/4)]}的值
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![已知x满足不等式2[㏒(1/2)^x]²+7㏒(1/2)^x+3≤0,求函数f(x)={㏒[2^(x/4)]}*{㏒[2^(x/4)]}的值](/uploads/image/z/14916702-30-2.jpg?t=%E5%B7%B2%E7%9F%A5x%E6%BB%A1%E8%B6%B3%E4%B8%8D%E7%AD%89%E5%BC%8F2%5B%E3%8F%92%EF%BC%881%2F2%EF%BC%89%5Ex%5D%26sup2%3B%2B7%E3%8F%92%281%2F2%29%5Ex%2B3%E2%89%A40%2C%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%3D%EF%BD%9B%E3%8F%92%5B2%5E%28x%2F4%29%5D%EF%BD%9D%2A%EF%BD%9B%E3%8F%92%5B2%5E%28x%2F4%29%5D%EF%BD%9D%E7%9A%84%E5%80%BC)
已知x满足不等式2[㏒(1/2)^x]²+7㏒(1/2)^x+3≤0,求函数f(x)={㏒[2^(x/4)]}*{㏒[2^(x/4)]}的值
已知x满足不等式2[㏒(1/2)^x]²+7㏒(1/2)^x+3≤0,求函数f(x)={㏒[2^(x/4)]}*{㏒[2^(x/4)]}的值
已知x满足不等式2[㏒(1/2)^x]²+7㏒(1/2)^x+3≤0,求函数f(x)={㏒[2^(x/4)]}*{㏒[2^(x/4)]}的值
设㏒(1/2)^x=x㏒(1/2)=-x㏒2=t;
则原不等式化为:2t^2+7t+3≤0,则-3≤t≤-1/2,即1/2≤x㏒2≤3;
f(x)={㏒[2^(x/4)]}*{㏒[2^(x/4)]}=1/16(x㏒2*x㏒2)
则1/64≤f(x)≤9/16.
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