设函数f(x)=log(a)x(a>0,a≠0),若f(x1x2…x2012)=9,则f(x1^2)+(x2^2)+…+f(x2012^2)的值为
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/01 06:07:32
![设函数f(x)=log(a)x(a>0,a≠0),若f(x1x2…x2012)=9,则f(x1^2)+(x2^2)+…+f(x2012^2)的值为](/uploads/image/z/10141325-53-5.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dlog%28a%29x%28a%3E0%2Ca%E2%89%A00%29%2C%E8%8B%A5f%28x1x2%E2%80%A6x2012%29%3D9%2C%E5%88%99f%28x1%5E2%29%2B%28x2%5E2%29%2B%E2%80%A6%2Bf%28x2012%5E2%29%E7%9A%84%E5%80%BC%E4%B8%BA)
设函数f(x)=log(a)x(a>0,a≠0),若f(x1x2…x2012)=9,则f(x1^2)+(x2^2)+…+f(x2012^2)的值为
设函数f(x)=log(a)x(a>0,a≠0),若f(x1x2…x2012)=9,则f(x1^2)+(x2^2)+…+f(x2012^2)的值为
设函数f(x)=log(a)x(a>0,a≠0),若f(x1x2…x2012)=9,则f(x1^2)+(x2^2)+…+f(x2012^2)的值为
f(x1^2)+(x2^2)+…+f(x2012^2)
=loga(x1^2...x2012^2)
=2loga(x1...x2012)
=2f(x1...x2012)
=2*9
=18
f(x1^2)+(x2^2)+…+f(x2012^2)
=log(a)x1^2+log(a)x2^2+....+log(a)x^2012^2
=2[log(a)x1+log(a)x2+....+log(a)x2012]
=2log(a)(x1x2...x2012)
=2*9
=18
易知f(x1x2…x2012)=logx1+logx2+…+log2012
∴f(x1²)+(x2²)+…+f(x2012²)=2(logx1+logx2+…+log2012)=18
因为f(x1x2…x2012)=9
f(x1^2)=2log(a)x1=2f(x1)
f(x2^2)=2log(a)x2=2f(x2)
f(x2012^2)=2log(a)x2012=2f(x2012)
f(x1^2)+(x2^2)+…+f(x2012^2)
=2f(x1)+2f(x2)+……+2f(x2012)
=2log(x1x2…x2012)
=2f(x1x2…x2012)
=18