人教B版数学高中必修第二册同步练习4.2.2 对数运算法则

4.2.2 对数运算法则必备知识基础练1.已知a>0,a≠1,x>y>0,n∈N+,下列各式:①(logax)n=nlogax;②logax=-loga1x;③logaxlogay=logaxy;④nlogax=1nlogax;⑤1nlogax=loganx;⑥logax=loganxn;⑦logax-yx+y=-logax+yx-y.其中成立的有(  )A.3个B.4个C.5个D.6个2.1log1419+1log1513等于(  )A.lg3B.-lg3C.1lg3D.-1lg33.(多选题)若10a=4,10b=25,则下列结论正确的是(  )A.a+b=2B.b-a=1C.ab>8lg22D.b-a>lg64.lg52+lg4-13-1=     . 5.若a=log43,则2a+2-a=     ,1a+1=     . 6.计算:(1)lg2+lg5-lg8lg50-lg40;(2)log28+lg11000+ln3e2+21-12log23+(lg5)2+lg2lg50.关键能力提升练7.设m=log30.5,n=log0.30.5,则(  ) A.m+n>0B.m+nmnD.m+nlg6,∴b-a>lg6.∴ab=4lg2lg5>4lg2lg4=8lg22.4.-2 lg52+lg4-13-1=lg10-3=1-3=-2.5.433 log312 ∵a=log43=log23,∴2a+2-a=2log23+2-log23=3+13=433.∵1a=log34,1=log33,∴1a+1=log34+log33=log312.6.解(1)原式=lg2×58lg5040=lg54lg54=1.(2)原式=3-3+23+2÷212log23+(lg5)2+lg2(lg5+1)=23+233+lg5(lg5+lg2)+lg2=53+233.7.BC 因为m=log30.50,所以mn0,∴logx5x=(logx5)2.∴12logx5x=(logx5)2.∴2(logx5)2-logx5-1=0,即(2logx5+1)(logx5-1)=0,∴logx5=-12或logx5=1.∵-logx5>0,∴logx5