Question

1．實(shí)數(shù)x，y滿足$\left\{\begin{array}{l}{xy≤64}\\{x≥2}\\{y≥2}\end{array}\right.$，則z=log₂x+log₂y的最小值是2．

Answer 1

分析 由x，y滿足$\left\{\begin{array}{l}{xy≤64}\\{x≥2}\\{y≥2}\end{array}\right.$，可得4≤xy≤64，利用對(duì)數(shù)函數(shù)的性質(zhì)求得z=log₂x+log₂y的最小值．

解答 解：∵$\left\{\begin{array}{l}{xy≤64}\\{x≥2}\\{y≥2}\end{array}\right.$，∴4≤xy≤64，
則z=log₂x+log₂y=log₂xy≥log₂4=2，
∴z=log₂x+log₂y的最小值是2．
故答案為：2．

點(diǎn)評(píng) 本題考查簡單的線性規(guī)劃，考查了不等式的性質(zhì)，考查對(duì)數(shù)函數(shù)的單調(diào)性，是基礎(chǔ)題．