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_数学解答

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

人气：150 ℃　时间：2020-06-08 04:16:36

解答

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