2.2对数函数2.2.1对数与对数运算第1课时对数课时过关·能力提升基础巩固1.log5b=2化为指数式是()A.5b=2B.b5=2C.52=bD.b2=5答案:C2.3b=5化为对数式是()A.logb3=5B.log35=bC.log5b=3D.log53=b答案:B3.对数lne2的值为()A.2B.eC.10D.e2答案:A4.已知logx8=3,则x的值为()A.12B.2C.3D.4解析:由题意,得x3=8=23,即x=2.答案:B5.若loga7√b=c(a>0,且a≠1,b>0),则有()A.b=a7cB.b7=acC.b=7acD.b=c7a解析:∵loga7√b=c,∴ac=7√b.∴(ac)7=(7√b)7.∴a7c=b.答案:A6.log23278=.解析:设log23278=m,则(23)m=278.又278=(32)3=(23)-3,∴(23)m=(23)-3,∴m=-3,即log23278=-3.答案:-37.已知log2x=3,则x-13=.解析:∵log2x=3,∴x=23=8,∴x-13=8-13=(23)-13=2-1=12.答案:128.若log31-2x9=0,则x=.解析:由题意,得1-2x9=1,解得x=-4.答案:-49.21+log23+log3127=.解析:令log3127=x,∴3x=127=3-3,∴x=-3.∴原式=2·2log23+log3127=2×3-3=3.答案:310.求值:(3√2)6+log33+log1216.解:设log1216=t,则(12)t=16,∴2-t=24,∴t=-4.∴原式=263+1-4=1.11.求下列各式中的x.(1)logx27=32;(2)log2x=-23;(3)logx(3+2❑√2)=-2;(4)log5(log2x)=0;(5)x=log2719.解:(1)由logx27=32,得x32=27,故x=2723=32=9.(2)由log2x=-23,得2-23=x,故x=13√22=3√22.(3)由logx(3+2❑√2)=-2,得3+2❑√2=x-2,即x=(3+2❑√2)-12=❑√2-1.(4)由log5(log2x)=0,得log2x=1,故x=21=2.(5)由x=log2719,得27x=19,即33x=3-2,故x=-23.能力提升1.若7x=8,则x等于()A.87B.log87C.log78D.log7x答案:C2.2-3=18化为对数式为()A.log182=-3B.log18(-3)=2C.log218=-3D.log2(-3)=18答案:C3.在log(x-2)(5-x)中,实数x的取值范围是()A.(-∞,2)∪(5,+∞)B.(2,3)∪(3,5)C.(2,5)D.(3,4)解析:由{5-x>0,x-2>0,x-2≠1,得20),则t2-6t-7=0,解得t=7或t=-1(舍去),∴3x=7.∴x=log37.答案:log377.方程log2(log3(x+1))=0的解x=.解析:∵log2(log3(x+1))=0,∴log3(x+1)=1,∴x+1=3,解得x=2.答案:2★8.求下列各式的值:(1)log2(log3(log464));(2)log2.56.25-3log32+(14)-12.解:(1)∵43=64,∴log464=3,∴log2(log3(log464))=log2(log33)=log21=0.(2)令log2.56.25=x,∴2.5x=6.25=2.52,∴x=2,∴log2.56.25-3log32+(14)-12=2-2+(2-2)-12=2-2+21=2.
