如果a大于0b大于0,证明lg((a+b)/2)大于等于(lga+ lgb)/2

问题描述:

如果a大于0b大于0,证明lg((a+b)/2)大于等于(lga+ lgb)/2

lg[(a+b)/2]
≥lg[2(根号ab)/2]
=lg根号ab
=lga^(1/2)+lgb^(1/2)
=1/2(lga+lgb)
=(lga+lgb)/2
命题得证看不明白lg[(a+b)/2]≥lg[2(根号ab)/2],a+b≥2根号(ab)=lg根号ab,分子分母同时除以2=lga^(1/2)+lgb^(1/2) ,根号(ab)=(ab)^(1/2)=a^(1/2)*b^(1/2)=1/2(lga+lgb) ,lga^(1/2)=1/2lga,lgb^(1/2)=1/2lgb=(lga+lgb)/2命题得证还有哪里不懂