(f(x1)+f(x2))/2=(lgx1+lgx2)/2=log(x1*x2)^0.5
f[(x1+x2)/2]=lg((x1+x2)/2)=lg(x1+x2)-lg2
x1>0 x2>0
x1+x2>=2(x1x2)^0.5
(x1+x2)/2>=(x1x2)^0.5
1/2[f(x1)+f(x2)>=f[(x1+x2)/2]
(f(x1)+f(x2))/2=(lgx1+lgx2)/2=log(x1*x2)^0.5
f[(x1+x2)/2]=lg((x1+x2)/2)=lg(x1+x2)-lg2
x1>0 x2>0
x1+x2>=2(x1x2)^0.5
(x1+x2)/2>=(x1x2)^0.5
1/2[f(x1)+f(x2)>=f[(x1+x2)/2]