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      2. 對(duì)數(shù)與對(duì)數(shù)運(yùn)算測(cè)試題及答案

        時(shí)間:2021-06-11 14:09:36 試題 我要投稿

        對(duì)數(shù)與對(duì)數(shù)運(yùn)算測(cè)試題及答案

          1.2-3=18化為對(duì)數(shù)式為()

        對(duì)數(shù)與對(duì)數(shù)運(yùn)算測(cè)試題及答案

          A.log182=-3B.log18(-3)=2C.log218=-3D.log2(-3)=18解析:選C.根據(jù)對(duì)數(shù)的定義可知選C.

          2.在b=log(a-2)(5-a)中,實(shí)數(shù)a的.取值范圍是()A.a(chǎn)>5或a0,a=b≠1解析:選D.a>0且a≠1,b>0,a1=b.

          2.若loga7b=c,則a、b、c之間滿足()A.b7=acB.b=a7cC.b=7acD.b=c7a解析:選B.loga7b=c?ac=7b,∴b=a7c.

          3.如果f(ex)=x,則f(e)=()A.1B.eeC.2eD.0解析:選A.令ex=t(t>0),則x=lnt,∴f(t)=lnt.∴f(e)=lne=1.

          4.方程2log3x=14的解是()A.x=19B.x=x3C.x=3D.x=9解析:選A.2log3x=2-2,∴l(xiāng)og3x=-2,∴x=3-2=19.

          5.若log2(log3x)=log3(log4y)=log4(log2z)=0,則x+y+z的值為()A.9B.8C.7D.6解析:選A.∵log2(log3x)=0,∴l(xiāng)og3x=1,∴x=3.同理y=4,z=2.∴x+y+z=9.

          6.已知logax=2,logbx=1,logcx=4(a,b,c,x>0且≠1),則logx(abc)=()A.47B.27C.72D.74解析:選D.x=a2=b=c4,所以(abc)4=x7,所以abc=x74.即logx(abc)=74.

          7.若a>0,a2=49,則log23a=________.解析:由a>0,a2=(23)2,可知a=23,∴l(xiāng)og23a=log2323=1.答案:18.若lg(lnx)=0,則x=________.解析:lnx=1,x=e.答案:e

          9.方程9x-6?3x-7=0的解是________.解析:設(shè)3x=t(t>0),則原方程可化為t2-6t-7=0,解得t=7或t=-1(舍去),∴t=7,即3x=7.∴x=log37.答案:x=log37

          10.將下列指數(shù)式與對(duì)數(shù)式互化:(1)log216=4;(2)log1327=-3;(3)log3x=6(x>0);(4)43=64;(5)3-2=19;(6)(14)-2=16.解:(1)24=16.(2)(13)-3=27.(3)(3)6=x.(4)log464=3.(5)log319=-2.(6)log1416=-2.

          11.計(jì)算:23+log23+35-log39.解:原式=23×2log23+353log39=23×3+359=24+27=51.

          12.已知logab=logba(a>0,且a≠1;b>0,且b≠1).求證:a=b或a=1b.證明:設(shè)logab=logba=k,則b=ak,a=bk,∴b=(bk)k=bk2.∵b>0,且b≠1,∴k2=1,即k=±1.當(dāng)k=-1時(shí),a=1b;當(dāng)k=1時(shí),a=b.∴a=b或a=1b,命題得證.

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