Question

已知x，y為正實(shí)數(shù)，則下列結(jié)論正確的是（　�。�

A、2log2x+log2y=2log2x?2log2y=x-y

B、2log2(x+y)=2log2x?2log2y=x+y

C、2log2x?log2y=2log2x+2log2y=x?y

D、2log2(xy)=2log2x?2log2y=x?y

Answer 1

分析：利用對(duì)數(shù)的運(yùn)算性質(zhì)log_am+log_an=log_amn；alogan=n與指數(shù)的運(yùn)算性質(zhì)a^m+n=a^m•aⁿ，判斷可得答案．

解答：解：對(duì)A，2log2x+log2y=2log2xy=xy，∴A錯(cuò)誤；
對(duì)B，2log2(x+y)≠2log2x•log2y，∴B錯(cuò)誤；
對(duì)C，2log2xy≠2log2x•2log2y，∴C錯(cuò)誤；
對(duì)D，2log2xy=2log2x+log2y=2log2x•2log2y=xy，∴D正確，
故選D．

點(diǎn)評(píng)：本題考查了指數(shù)與對(duì)數(shù)的運(yùn)算性質(zhì)，指數(shù)與對(duì)數(shù)的運(yùn)算性質(zhì)要熟練掌握．