1、学业分层测评(十五) 对数(建议用时:45分钟)学业达标一、选择题1若logxz,则()Ay7xzByx7zCy7xDyz7x【解析】由logxz,得xz,yx7z.【答案】B2方程2 log3x的解是()A9 B. C. D.【解析】2 log3x22.log3x2.x32.【答案】D3log5log3(log2x)0,则x等于() 【导学号:97030096】A. B. C. D.【解析】log5log3(log2x)0,log3(log2x)1,log2x3.x238.x8.【答案】C4设2a5bm,且2,则m()A.B10C20D100【解析】logm2logm5logm102,m21
2、0,又m0,m.故选A.【答案】A5下列各式:lg(lg 10)0;lg(ln e)0;若10lg x,x10;若log25x,得x5.其中正确的个数有()A1个B2个C3个D4个【解析】底的对数为1,1的对数为0,故正确,0和负数没有对数,故错误,中10lg x,应该有x1010,所以只有正确【答案】B二、填空题6(2016湘潭高一检测)已知a,则loga_.【解析】a2,a4,loga4.【答案】47已知logx3,则x_.【解析】logx3,x3.x.【答案】8使log(x1)(x2)有意义的x的取值范围是_【解析】要使log(x1)(x2)有意义,则x1且x2.【答案】(1,2)(2,
3、)三、解答题9求下列各式中x的值(1)log5(log3x)0;(2)log3(lg x)1;(3)lnlog2(lg x)0.【解】(1)设tlog3x,则log5t0,t1,即log3x1,x3.(2)log3(lg x)1,lg x3,x1031 000.(3)lnlog2(lg x)0,log2(lg x)1,lg x2,x102100.10若logxm,logym2,求的值 【导学号:97030097】【解】logxm,mx,x22m.logym2,m2y,y2m4.2m(2m4)416.能力提升1已知x2y24x2y50,则logx(yx)的值是()A1B0CxDy【解析】由x2y24x2y50,则(x2)2(y1)20,x2,y1,logx(yx)log2(12)0.【答案】B2设g(x)则g_.【解析】0,gln .而ggeln .【答案】3若loga2m,loga3n,则a2mn_.【解析】loga2m,loga3n,am2,an3,a2mn(am)2an22312.【答案】124已知二次函数f(x)(lg a)x22x4lg a的最大值为3,求a的值【解】原函数式可化为f(x)lg a24lg a.f(x)有最大值3,lg a0,且4lg a3,整理得4(lg a)23lg a10,解之得lg a1或lg a.又lg a0,lg a. a10.