1、学业分层测评(十六)(建议用时:45分钟)学业达标一、选择题1若xy2(y0,且y1),则必有()Alog2xyBlog2yxClogxy2Dlogyx2【解析】由xy2得logyx2.【答案】D2若logxz,则()Ay7xzByx7zCy7xzDyz7x【解析】由logxz,得xz,所以x7zy.【答案】B3若3log3x29,则x()A3B3C3D2【解析】由3log3x2x29,得x3.【答案】C4(2016嘉兴高一检测)计算:23log2335log39()A15B51C8D27【解析】原式232log23353log398324242751.【答案】B5已知loga 2m,loga
2、 3n,则a2mn等于()A5 B7 C10D12【解析】am2,an3,a2mna2man(am)2an12.故选D.【答案】D二、填空题6方程log2(2x1)2的解为x_.【解析】由log2(2x1)2,则2x1224,故x.【答案】7ln 1log (1)_.【解析】ln 1log(1)011.【答案】18已知log7 log3(log2x)0,那么x-_.【解析】由题意得log3(log2x)1,即log2x3,转化为指数式则有x238,x8.【答案】三、解答题9求下列各式中的x.(1)log2(log5x)0;(2)logx 27.【解】(1)由log2(log5x)0得log5x
3、1,x5.(2)由logx 27得x27,x27,即x(33),x3481.10计算下列各式:(1)10lg 3log4 12log2 6;(2)22log2332log3 9.【解】(1)10lg 3log4 12log2 63069.(2)22log2 332log3 9222log2 34312113. 能力提升1(2016临沂高一检测)若lga5.21,lgb3.21,则等于()A10B.C.D100【解析】由lga5.21,lgb3.21,得a105.21,b103.21,则102.【答案】C2. 1log0.54的值为() 【导学号:04100053】A6B. C8D.【解析】1l
4、og0.541log4248.故选C.【答案】C3方程9x63x70的解是_【解析】令t3x,则t0,则方程变为t26t70,解得t7或1(舍去)则3x7,得xlog37.【答案】log374求下列对数的值:(1)ln e2;(2)log81;(3)log1.52.25;(4)lg ;(5)log816;(6)ln (eln 1)【解】(1)设ln e2x,则exe2,x2,ln e22.(2)设log81x,则x8192,即9x92,x2,即log812.(3)1.522.25,log1.52.252.(4)104,lg 4.(5)设log816x,则8x16,即23x24,3x4,即x,log816.(6)ln 10,ln (e0)ln 10,ln eln 10.