1、1.的值为()A1B1C. D.答案C2(2013陕西)设a,b,c均为不等于1的正实数,则下列等式中恒成立的是()AlogablogcblogcaBlogablogcalogcbCloga(bc)logablogacDloga(bc)logablogac答案B解析利用对数的换底公式进行验证,logablogcalogcalogcb,故选B.3(2013课标全国)设alog36,blog510,clog714,则()AcbaBbcaCacbDabc答案D解析alog361log32,blog5101log52,clog7141log72,则只要比较log32,log52,log72的大小即可,
2、在同一坐标系中作出函数ylog3x,ylog5x,ylog7x的图像,由三个图像的相对位置关系,可知abc,故选D.4log2sinlog2cos的值为()A4B4C2D2答案C解析log2sinlog2coslog2(sincos)log2(sin)log22,故选C.5当0x()1xBlog(1x)(1x)1C01x20答案C解析方法一:考查答案A:0x1x.()x1()1x,故A不正确;考查答案B:0x1,01x1.log(1x)(1x)0,故B不正确;考查答案C:0x1,0x21,01x21,故C正确;考查答案D:01x1.log(1x)(1x)0.故D不正确方法二:(特值法)取x,验
3、证立得答案C.6若0a0B增函数且f(x)0D减函数且f(x)0答案D解析0a1时,ylogau为减函数,又ux1增函数,f(x)为减函数;又0x1,又0a1,f(x)1,b1,p,则ap_.答案logba11若loga(x1)loga(x1),则x_,a_.答案(1,)(1,)12若loga(a21)loga2a0,则实数a的取值范围是_答案(,1)解析a211, loga(a21)0,0a1.又loga2a0,2a1,a.实数a的取值范围是(,1)13若正整数m满足10m1251210m,则m_.(lg20.301 0)答案155解析由10m1251210m,得m1512lg2m.m115
4、4.12m.m155.14若函数f(x)loga(x1)(a0,a1)的定义域和值域都是0,1,则a_.答案2解析f(x)loga(x1)的定义域是0,1,0x1,则1x12.当a1时,0loga1loga(x1)loga21,a2;当0af(1),且log2f(x)f(1)答案(1)x时,最小值(2)0x1解析(1)f(x)x2xb,f(log2a)(log2a)2log2ab.由已知(log2a)2log2abb,log2a(log2a1)0.a1,log2a1,a2.又log2f(a)2,f(a)4.a2ab4,b4a2a2.故f(x)x2x2.从而f(log2x)(log2x)2log2x2(log2x)2.当log2x,即x时,f(log2x)有最小值.(2)由题意0x1.5 / 5