f(x)=loga(x),(a>0,且a≠1).若f(x1x2…x2005)=8,那么f(x1^2)+f(x2^2)+…+f(x2005^2)=?

熱心網友

f(x1x2…x2005)=loga(x1x2…x2005)=loga(x1)+loga(x2)+…+loga(x2005)=8又f(x^2)=loga(x^2)=2loga(x)所以f(x1^2)+f(x2^2)+…+f(x2005^2)=2[loga(x1)+loga(x2)+…+loga(x2005)]=16

熱心網友

設f(x1^2)+f(x2^2)+…+f(x2005^2)=yf(x1^2)+f(x2^2)+…+f(x2005^2)-f(x1x2…x2005)=y-8=f(x1x2…x2005)所以y=16