题目内容：

已知a>1且a^(lgb)=4次根号下2,求log2(ab)的最小值
a^(lgb)=2^1/4,
两边取以2为底的对数得:log2(a^(lgb))=log2(2^1/4),即lgblog2(a)=1/4,
所以lgb=1/4log2(a),而log2(ab)=log2(a)+log2(b)=log2(a)+lgb/lg2,
所以log2(ab)=log2(a)+1/4log2(a)lg2,因为a>1,所以log2(a)>log2(1)=0,
所以log2(a)+1/4log2(a)lg2≥2√[log2(a)/4log2(a)lg2]=2√[1/4lg2]=√(1/lg2)=
√(log2(10)),即log2(ab)最小值为√[log2(10)]