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

显示全部楼层 · 2013-2-2 14:44:16

f(x1^2)+(x2^2)+…+f(x2012^2)=loga(x1^2...x2012^2)=2loga(x1...x2012)=2f(x1...x2012)=2*9=18...

千问 · 2013-2-2 14:44:16

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...

千问 · 2013-2-2 14:44:16

因为f(x1x2…x2012)=9f(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...

千问 · 2013-2-2 14:44:16

解：易知f(x1x2…x2012)=logx1+logx2+…+log2012∴f(x12)+(x22)+…+f(x20122)=2(logx1+logx2+…+log2012)=18...