设函数f(x)=loga(x)(a>0且a不等于1)若f(x1.x2.x2009)=8则f(x1^2)+.f(x2009^2)等于几

问题描述:

设函数f(x)=loga(x)(a>0且a不等于1)若f(x1.x2.x2009)=8则f(x1^2)+.f(x2009^2)等于几
等16么

f(x1.x2.x2009)=log a(x1.x2.x2009)=log a x1+log a x2+……+log a(x2009)=8
f(x1^2)+.f(x2009^2)=log a(x1^2)+……+log a(x2009^2)=2[log a(x1)+……+log a(x2009)]
=2×8=16