4.指对数比较大小

指数与对数函数、比较大小1.指数与对数基本运算axNlogaNxarasarsarrsaasloga(MN)logaMlogaN;logaMlogaMlogaN;Nnlogambnmlogab(a、b均大于0且不等于1，m0,nR)logaNarsars1manmana0,m,nN*,且n1logbN(a、b均大于0且不等于1，N0)logba特殊:log10xlgx,logexlnx(e2.718)x2.指数与对数函数的图像及性质指数:ya(a0且a1),对数:ylogax(a0且a1)考点一指、对数式的化简与求值1.已知函数f(x)log2(x2a).若f(3)1,则a_______.log2x,x0,12.已知函数f(x)x则f(f(1))f(log3)的值是( )231,x0, A. 2 B. 3 C. 4 D. 5113.设2a5bm,则2,则m等于( )ab A. 10 B. 10 C. 20 D. 100题组训练1.化简下列各式:5 1ab23ab4ab36lg2lg5lg8 2lg50lg4013121231221log210log7232 3log5433712.设log23,则3x3x的值为( )x8357 A. B. C. D. 3223考点二指、对数比较大小11.设alog3e,be1.5,clog1,则( )34 A. bac B. cab C. cba D. acb12.设a,blog23,c20.3,则( )2 A. acb B. cba C.cab D. bac3.设a0.50.4,blog0.50.3,clog80.4,则( ) A. abc B. cba C. cab D. acb0.234

4.设a,b,clog3log34,则( )

434 A. bac B. cab C. cba D. acb1

5.设a20.11,blg,clog30.3,则( )

4 A. bac B. cab C.acb D. cba1

6.设a21.2,b2log52,cln,则( )

3

A. cba B. cab C. bac D. acb7.设alog412,blog515,clog618,则( )

A. cba B. cab C. bac D. acb8.已知logx33,logy76,z7,则( )

A. xzy B. zxy C. xyz D. zyx

170.50.4

题组训练

1.设a2log23,blog0.30.4,c3ln2,则a,b,c的大小关系为( ) A.bac B.acb C.bca D.abc2.设a20210.2,b0.22021,clog20210.2,则( ) A. cba B. cab C. abc D. bca3.设2alog3bc,则a,b,c的大小关系为( ) A. acb B. cab C. abc D. bca

考点三指、对数比较大小与函数的性质

x

1

1.已知函数f(x)=,记af(20.3),bf2,cf(log25),则 2

A. b>a>c B. a>b>c C. c>b>a D.cab

2.已知函数f(x)是定义在R上的偶函数,且在-,0上单调递减,若af(log bf(log24.1),cf(20.5),则( )

A. c>b>a B. cab C. b>a>c D. a>b>c

1

2),5

3.已知定义在R上的函数f(x)=x2,若af(log3 A.a>b>c B.c>b>a C.b>a>c D.cabx5),bf(log31),cf(ln3),则( ) 24.已知奇函数f(x)在R上是增函数,g(x)xf(x).若ag(log25.1),bg(20.8),cg(3),则( ) A.a>b>c B.c>b>a C. cab D.b>a>c5.已知定义在R上的函数f(x),满足条件yf(x1)是关于x的偶函数,且当x1时,11 f(x)1,若af(log32),bf(log3),cf(3),则( )22 A.a>b>c B.c>b>a C. b>a>c D. cab6.已知定义在R上的函数f(x1)的图象是关于x=1对称,且当x>0时, f(x)单调递减, 若af(log0.53),bf(0.51.3),cf(0.76),则( ) A. cab B. c>b>a C. b>a>c D. a>b>c题组训练1111.已知偶函数f(x)在0,单调递减,af(loge),bf(log3),cf(log1),则( ) 3ee9 A.b>a>c B.acb C.bac D.a>b>c2.已知函数f(x)在R上单调递减,且f(-x)=-f(x),若a-f(log3 A.a>b>c B.c>b>a C.b>a>c D.cab2x1),bf(log39.1),cf(20.8),则( ) 1011733.已知函数f(x)=lg(4x),记af(log3),bf(),cf(20.8),则( ) 24 A.a>b>c B. b>a>c C.c>b>a D.cab1.已知alog52,blog0.50.2,c0.50.2,则( ) A. acb B. abc C. bca D. cab 2.已知alog27,blog38,c0.30.2,则( ) A. cba B. abc C. bca D. cab 3.已知alog2e,bln2,clog121,则( )3 A. acb B. abc C. bca D. bac 7114.已知alog3,b,clog1,则( )2435 A. acb B. abc C. bca D. bac135.已知alog2,blog1,c2,则( )2 A. acb B. abc C. bca D. bac16.已知a21.2,b,c2log52,则( )2 A. cba B. abc C. bca D. bac17.已知a5log23.4,b5log43.6,c,则( )5 A. acb B. abc C. bca D. bac8.已知alog23.6,blog43.2,clog43.6,则( ) A. acb B. bca C. abc D. bac9.已知alog54,blog53,clog45,则( ) A. acb B. abc C. bca D. bac110.已知alog12,blog13,c,则( )232 A. acb B. bca C. abc D. bac11.已知f(x)是定义在R上的偶函数,且f(x)在0,+内单调递减,则( ) A.f(0)f(log32)f(log23) B.f(log32)f(0)f(log23) C.f(log23)f(log32)f(0) D.f(log32)f(log23)f(0)1212.已知函数f(x)x,若af(log26),bf(log2),cf(30.5),则( )x9 A. acb B. bca C. abc D. cba13.已知函数f(x)exex,若3alog3bc,则( ) A.f(a)f(b)f(c) B.f(b)f(c)f(a) C.f(a)f(c)f(b) D.f(c)f(b)f(a)14.已知函数f(x)e,若af(sinx0.32log30.30.83),bf(23),cf(log13),则( )42 A. bac B. bca C. abc D. cba1215.偶函数f(x)在0,2上递增,若af(1),bf(log1),cf(log2),则( )224 A. bac B. bca C. cab D. cba16.已知f(x)是定义在R上的偶函数,当x0时,f(x)2018x,若af(ln3e),bf(0.22 cf(),则( )3 A. bca B. bac C. cab D. cba10.3),