1、第三章44.1一、选择题1若log8x,则x的值为()A.B4C2 D.答案A解析log8x,x822,故选A.2当a0,a1时,下列结论正确的是()若MN,则logaMlogaN;若logaMlogaN,则MN;若logaM2logaN2,则MN;若MN,则logaM2logaN2.ABCD答案C解析M0时不对;正确;应为MN;M0时不对3lg20lg50的值为()A70B1000C3 D.答案C解析lg20lg50lg10003.故选C.4已知alog32,那么log382log36用a表示是()Aa2B5a2C3a(1a)2D3aa21答案A解析log382log36log3232(lo
2、g32log33)3log322(log321)3a2(a1)a2.故选A.5若logac,则a,b,c满足关系式()Ab7acBba7cCb7acDbc7a答案B解析logac,ac,ba7c.6()1log0.54的值为()A6 B.C8 D.答案C解析原式()1()4248.二、填空题7求值:(1)810.5log35_;(2)5log51003_;(3)27log32_.答案(1)25(2)(3)72解析(1)810.5log35(34) 0.5log3532log35(3log35)25225.(2)5 log510033.(3)27log32(33)log32323log3232(
3、3 log32)39872.8已知log32a,则2log36log30.5_.答案a2解析原式2log3(23)log32(log32log33)log32log322a2.三、解答题9计算下列各式的值:(1)log2log212log242;(2)lg52lg8lg5lg20(lg2)2.解析(1)原式log2log212log2log2(12)log2(12)log2log22.(2)原式2lg52lg2lg5(1lg2)(lg2)22(lg5lg2)lg5lg2(lg5lg2)2lg5lg2213.10(2022德阳高一检测)计算:log28lgln21log23(lg5)2lg2lg
4、50.解析原式3322log23(lg5)2lg2(lg51)lg25(1lg5)(1lg5).一、选择题1方程log3(x1)log9(x5)的解为()Ax1Bx1或x4Cx4Dx1且x4答案C解析确定要留意对数的真数大于零,即,解得x4,选C.2假如f(10x)x,则f(3)等于()Alog310Blg3C103D310答案B解析令10x3,xlg3.故选B.二、填空题3(1)已知a(a0),则a_.(2)已知m0,且10xlg(10m)lg,则x_.答案(1)3(2)0解析(1)由a(a0),得a()()3,所以a()33.(2)10xlg(10m)lg101.所以x0.4若正数m,满足
5、10m1251210m,则m_.(lg20.3010)答案155解析10m1251210m,m1512lg2m,154.112m155.112,又mN,m155.三、解答题5计算下列各式的值:(1)lg5log36lg20log32;(2)log213lg1000log21;(3);(4)(lg5)22lg2(lg2)2.解析(1)原式(lg5lg20)(log36log32)lg100log33213.(2)原式(log213log217)lg103134.(3)原式.(4)原式(lg5lg2)(lg5lg2)2lg2lg10lglg4lg(4)lg101.6已知log2(log3(log4x)log3(log4(log2y)0,求xy的值解析log2(log3(log4x)log3(log4(log2y)0,log3(log4x)1,log4(log2y)1,log4x3,log2y4,x43,y24,xy4324262480.7求31log3624log23103lg3()log34.解析原式313log36242log23(10lg3)332log343616333(3log34)2361633342184827.