1、第三章基本初等函数()3.2对数与对数函数3.2.1对数及其运算第二课时对数的运算及应用课时跟踪检测A组基础过关1计算2log63log64的结果是()A2 Blog62Clog63 D3解析:2log63log64log69log64log6362,故选A答案:A2计算log3lg 25lg 47(9.8)0值为()A6 B8C D解析:原式log33lg 1002123,故选D答案:D3已知abM(a0,b0,M1),logM bx,则logM a的值为()A B1xC1x Dx1解析:abM,logM(ab)logMM1.又logM(ab)logMalogMb,logMa1logMb1x
2、.答案:C4已知2x3,log4y,则x2y的值为()A3 B8C4 Dlog48解析:x2ylog232log4log49log42log4log4643.答案:A5已知2a3bk(k1),且2abab,则实数k的值为()A6 B9C12 D18解析:由2a3bk得,alog2k,blog3k,由2abab得,2log2klog3klog2klog3k .由换底公式得, .k1,lg k0, .2lg 3lg 2lg k,k18.答案:D6log32log310()A0 B1C2 D3解析:原式log3log3100log392.答案:C7log29log34_.解析:log29log34l
3、og2322log234.答案:48计算:0.5204log45ln e5lg 200lg 2.解:原式12552lg 2lg 2.B组技能提升1已知log32a,3b5,则log3用a,b表示为()A(ab1) B(ab)1C(ab1) Db1解析:由3b5得, blog35,而log3(log3101)(log35log321)(ab1),故选A答案:A2设a0,a1,且xy0,n2,nN*,考虑下列等式(logax)nnlogax;loga(xy)logaxlogay;loga;logalogax;loga(xy)logaxlogay;ax;logaloga.其中正确的个数为()A2个
4、B3个C4个 D5个解析:正确,故选B答案:B3化简(1log63)2log62log618log64_.解析:原式1.答案:14已知3x5y15,则_.解析:由3x5y15,得log315x,log515y,log153log1551.答案:15(1)(lg 2)2lg 20lg 5log92log43;(2)2log32log3log3825log53.解:(1)原式(lg 2)2(2lg 2lg 5)lg 5(lg 2)22lg 2lg 5(lg 5)2(lg 2lg 5)2.(2)原式log34log3log385log35297.6设a,b,c为直角三角形的三条边,c为斜边,求log2log2的值解:a0,b0,c0,a2b2c2,原式log2log2log2log2log221.