已知a>1且a^(lgb)=4次根号下2,求log2(ab)的最小值
问题描述:
已知a>1且a^(lgb)=4次根号下2,求log2(ab)的最小值
答
a^(lgb)=2^(lgblog2(a))=2^(1/4) lgblog2(a)=log2(b)log2(a)/log2(10)=1/4 log2(a)log2(b)=log2(10)/4log2(ab)=log2(a)+log2(b)>=2√[log2(a)log2(b)]=2*(1/2)*√log2(10)=√log2(10)最小值√log2(10)