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??????1?23log89???? ? A? B?1 C? D?232log23
2352??log2[log1(log2x)]?log3[log1(log3y)]?log5[log1(log5z)]=0??x?y?z????????
A?z?x?y B?x?y?zC?y?z?x
3D?z?y?x3???x=2+1,?log4(x?x?6)??? ?A.351 B. C.0 D.242 4???lg2=a?lg3=b??2a?ba?2b2a?ba?2blg12??? ?A? B? C? D? 1?a?b1?a?b1?a?b1?a?blg15
5???2 lg(x?2y)=lgx?lgy??x??? ( ?A?1 B?4C?1?4D?4 ? y
6.??y=log1(2x?1)?????? ?A?(
2
211???) B??1???) C?( ?1] D?(???1)227?????y=log1 (ax?2x?1)????R????a??????? ?2
A?a ? 1 B?0?a? 1C?0?a?1 D?0?a?1 x5 e 8.??f(e)=x??f(5)??? ?A?e B?5C?ln5D?log5e9??f(x)?logax(a?0?a?1),?f?1(2)?1,?f(x)??????
A
B C
D10??y??log2(x2?ax?a)???(??,1???????a??????? ?A?[2? B??2?2 C?2?2? D?2?2 ??????
11????A?{x|x?1?0},B?{x|log2x?0|},?A?B??? ? A?{x|x?1} B?{x|x?0}C?{x|x??1} D?{x|x??1?x?1}2
12???y?lnx?1,x?(1,??)????? ?? x?1
ex?1ex?1ex?1ex?1y?x,x?(0,??)B?y?x,x?(0,??)C?y?x,x?(??,0)D?y?x,x?(??,0) e?1e?1e?1e?1A
??????13????log2.56.25?lg
211?log23?lne?2= ?10014???y=log4(x?1)(x?1?????? ?
0.90.815???m?1????(lgm)?(lgm)????
16???y =(log1x)?log1x?5 ? 2?x?4??????4422
??????17???y=loga(2?ax)???{0?1}??x??????a??????
2218?????f(x)=lg[(a?1)x?(a?1)x?1]??f(x)?????R????a?????.
219???f(x)=x?(lga?2)x?lgb?f(?1)=?2??x?R?f(x)?2x???????a???????f(x)???
??
20??0?x?1?a?0?a?1????|loga(1?x)|?|loga(1?x)|????
x21?????f(x)=loga(a?a)?a?1??1?????????????2???f(x)????????????3??
???????y=x???
22??????y=log2x????(??)??A?B?C????????????a?a?1?a?2???a?1???ABC???????
????
?????? ADBCB CDCBA AB
??????13.
??????
17.????????????2?ax?0??ax?2??a????????a?0?a?1??x?2513x0.90.8?y?8 ?14.y=1?2(x?R)? 15. (lgm)?(lgm)?16.242 a?????[0?1]????????2?1??a?2??2?ax?x?[0?1]???? a
?y=loga(2?ax)???[0?1]?????????????????a?1??1?a?2
22218??????(a?1)x?(a?1)x?1?0???x?R?????a?1?0?????????
2?5?a?1?0??a??1?a??a=?1?f(x)=0?????a=1?????? ?223?????(a?1)?4(a?1)?0
??a???????(????1]?(5???) 3
19?????f(?1)=?2 ???f(?1)=1?(lga?2)?lgb=?2???lga?lgb=1??
22a=10?a=10b? b??x?R?f(x)?2x??????x?(lga?2)x?lgb?2x??x?xlga?lgb?0??x?R????
222??=lga?4lgb?0????(1?lgb)?4lgb?0??(lgb?1)?0???lgb=1???????
22?b=10??a=100??f(x)=x?4x?1=(2?x)?3??x=?2??f(x) min=?3?
20.???????
|loga(1?x)|?|loga(1?x)|=|lg(1?x)1lg(1?x) |?||=(|lg(1?x)|?|lg(1?x)|) lga|lga|lga
?0?x?1??0?1?x?1?1?x
???=?112[(lg(1?x)?lg(1?x)]=?lg(1?x) |lga||lga|
2?0?x?1???lg(1?x)?0???
?|loga(1?x)|?|loga(1?x)|
??????? 12lg(1?x)?0? |lga|
|loga(1?x)|=|log(1?x)(1?x)| |loga(1?x)|
?0?x?1??0?1?x?1?x??|log(1?x)(1?x)|=?log(1?x)(1?x)=log(1?x)
?0?x?1??1?x?1?0?1?x?1
?0?(1?x)(1?x)?1??21 1?x1?1?x?0 1?x
?0?log(1?x) 1?log(1?x)(1?x)=1 1?x
?|loga(1?x)|?|loga(1?x)|
???????????
22?loga(1?x)?loga(1?x)=[loga(1?x)?loga(1?x)][loga(1?x)?loga(1?x)] =loga(1?x)loga21?x11?x2=lg(1?x)lg 21?x1?x|lga|
2?0?x?1??0?1?x?1?0?
221?x1?x2?1?lg(1?x)?0?lg?0 1?x1?x?loga(1?x)?loga(1?x)??|loga(1?x)|?|loga(1?x)|
?????????????
2?a?1??|loga(1?x)|?|loga(1?x)|=?loga(1?x)?loga(1?x)=?loga(1?x)
2?0?1?x?1?1?x??0?1?x?1
22?loga(1?x)?0???loga(1?x)?0
?0?a?1???0?x?1???loga(1?x)?0?loga(1?x)?0
2?|loga(1?x)|?|loga(1?x)|=|loga(1?x)?loga(1?x)|=loga(1?x)?0
??a?0?a?1????|loga(1?x)|?|loga(1?x)|
21.???(1)????(???1)????(???1)
(2)?1?x2?x1?a?1??ax2?ax1???a?ax2?a?ax1
x?loga(a?aax2)?loga(a?a1)
?f(x2)?f(x1)
?f(x)????(???1)?????
xxyy(3)????y=loga(a?a)(x?1)??a?a=a?x=loga(a?a)
?1x?f(x)=loga(a?a)(x?1)
x?f(x)????????????f(x)=loga(a?a)(x?1?????y=x???
22.??????????A?B?C???????(a?log2a)?(a?1?log2(a?1))?(a?2?log2(a?2))???ABC??? S=[log2a?log2(a?1)][log2(a?1)?log2(a?2)]??[log2a?log2(a?2)] 22
(a?1)21a(a?2)(a?1)21 ?log2?log22a(a?2)2[a(a?2)]2
11a2?2a?11?log(1?) ?log22222a?2a2a?2a
??a?1,??Smax?
1114log2(1?)?log2 2323
???????????????????
?????????????
??????????12??????4???48????????????????????????????
1???3a?2???log38?2log36?a?????
A?a?2 B?5a?2 C?3a?(1?a)2D? 3a?a
2
??A?
?3=2??a=log32
?: log38-2log36=log32-2log3(2*3) =3log32-2[log32+log33] =3a-2(a+1) =a-2
3
a
2?2loga(M?2N)?logaM?logaN??
M
????? N
1
A?B?4 C?1 D?4?1
4??B?
?2loga(M-2N?=logaM+logaN?
?loga(M-2N)=loga(MN????M-2N)=MN?
?M-4MN+4N=MN??m-5mn+4n=0?????n??(m)-5m+4=0,?x=m nnn?x2-5x+4=0?(x2
2
22
2
2222
?x??x?1?
??2loga(M?2N)?logaM?logaN???M-2N>0 M>0 N>0
?m=1????4 n1
?,nlog?ay???? a
1?x
11
A?m?nB?m?nC??m?n?D??m?n?
22
22
1?)x?m,log3???x?y?1,x?0,y?0??loga(
??D?
?loga(1+x)=m loga [1/(1-x)]=n?loga(1-x)=-n??????? loga [(1+x)(1-x)]=m-n
?loga(1-x2)=m-n ?? x2+y2=1?x>0?y>0, ? y2=1- x2?loga(y2)=m-n
?2loga(y)=m-n
4. ?x1?x2???lgx ?(lg3?lg2)lgx?lg3lg2 = 0?????x1x2???( )? (A)?lg3lg2 (B)?lg6 (C)?6 (D)?
2
1
6
??D
lg2x+?lg2+lg3?lgx+lg2lg3=0????x??[??lg2x??lgx)2???????x21
?lgx????X????????]
?lgx1 +lgx2= -a= -?lg2+lg3?? lg?x1x2?= -lg?23?
??lg?x1x
?= -lg6=lg2
111
??x1x2= ??x1?x2??? ? 666
?1
2
5???log7[log3(log2x)]?0???x A?
????
1 B
D
3??C
?log7?log3(log2X)?=0??log3(log2x)=1?log2x=3?x=8
6???lg2=a?lg3=b??
lg12
??? ?lg15a?
2b
1?a?b
C?
A?
2a?b
1?a?b
B?
2a?b
1?a?b
D?
a?2b
1?a?b
??C
lg12=lg3*2*2=lg3+lg2+lg2= 2a+b
?????2a+b)/(1-a+b)
7???y?log(2x?1)??????? A??
?2??1?
,1???1,???B??,1???1,????3??2??2??1?,???D??,??? ?3??2?
C??
??A
y?log(2x?1)
??????
??3x?2?0?x?3??2x?1?0?x?2??x?3,x?1 ??????
?2x?1?1?x?1???
?2?
,1???1,??? ?3?
8???y?log1(x2?6x?17)??????
2
A?RB??8,??? C????,?3? D??3,??? ????C ,y=(-?,-3?
?x-6x+17=x2-6x+9+8=(x-3)2+8?8??log
2
12
= log
12
?1
=(-1) log2= - log2 (?-
log2x???? log1x???? log1[(x-3)2+8] ???.,????
2
2
?x-6x+17=(x-3)2+8 ,x?????(x-3)2+8????? (x-3)2+8=0??,x=3, ????8, ?log1[(x-3)2+8]= log18= - log28= -3, ??? y?-3?y=(-?,-3?[??
2
Y=x
2
-6x+17 ??????3?8????Y???Y]
9??logm9?logn9?0???m,n????????
A?m?n?1 B?n?m?1C?0?n?m?1 D?0?m?n?1 ????C
??????????????????y=logax?a?0??a?1??????????x?????????????0?+??????R?????????? y=logax?a?0?
???????
a,c????????1?
10?logaA??0,
2
?1??a???????? 3
??2??2??2??2??2?
B? C?D??1,??,??,10,?,?????????????
3?3333????????
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??loga(x)????, 1=loga(a),?log
a
??2/3>a?????0<a<1???0<a<2/3
?a>1???loga(x)????? loga(2/3)<1??loga? ??2/3<a?????a>1????a>1?????0<a<3,a>1
a
2
?1,?loga(2/3)<loga(a) 3
11?????????0,2?????????? A?y?log1(x?
1) B?y?log2
2
C?y?log2
12D
?y?log(x?4x?5) x????D?
A? x+1??0,2?????? ?2???????????? ?????y????
??? B?
x2?1??0,2??????????<1???x<1??????0,2?? ????
???????????0,2????<1??
C?x??????2????????????y????
D??A???x2-4x+5=(x-2)+1,????2???0,2??????2??????????????????
12?????y=log1 (ax?2x?1)????R????a??????? ?2
2
2
A?a ? 1 B?0?a? 1????C?
C?0?a?1 D?0?a?1
+2x+1)????R
?ax+2x+1?>0,?g(x)=ax+2x+1,????g(x)=ax+2x+1??????????????,??g(x)?????Y??>0, ???????????,?a?0
????????0?????????x???,??x?????,???????0????(????<0, ?????x???,??x????) ?b-4ac=4-4a?0,??a?1?????a??????0?a?1?
??????0?a?1,???0?a?1?
??????????4??????4???16??????????????
2
222
113???log2.56.25?lg?lne?
100
????
21?log23= ?
???????e???2.71828??????????????????ln ???e??????ln1=0?lne=1? ?2?2
1og23
=x?????????????? log2x= (log23) ??x=3
1og23
1og23
=x, ?? x=3, ??2
=3.?
?2.5?
+ lg10
=
log2.5
2
1
log2.56.25?lg?lne?
100
2
1?log23
?3
+ lne
12
+2?2
1
1og23
3=2-3+
14???
y?log(x-1)(3-x)??????
????
?2???????????????0?????0??????1 ?
?????????1??????????????????????
??????1???? ?????????????????
?????
1???x?y??????( ) A?2lgx?lgy?2lgx?2lgy
lgy
C?2lgx?2lgx?2lgy
B?2lg(x?y)?2lgx2lgy D?2lg(xy)?2lgx2lgy
?? ?????????x?10?y?1,2lgx?lgy?2,2lg(xy)?2,2lgx
lgy
?2lgy?3,2lg(x?y)?2lg11,2lgx?1.
?? D
2????y?f(x)???y?ax(a>0?a?1)?????f(2)?1??f(x)?( )
1
A.2 C?log1 x
2
B?2x?2 D?log2x
?? ????f(x)?logax??f(2)?1??loga2?1? ?a?2??f(x)?log2x. ?? D
3???f(x)?log3x????y?f(x?1)???[2,8]????????????( )
A?2?1C?9?3
B?3?1 D?8?3
?? ?f(x)?log3x??f(x?1)?log3(x?1)? ?2?x?8??3?x?1?9. ?1?log3(x?1)?2. ?? A
4?????????( ) A?log0.56>log0.54
?1?
C?2.50<?2?2.5 D
??
B?90.9>270.48 ?0.60.5>log0.60.5
?? ?90.9?32.7,270.48?31.44??y?3x?(?????)???????32.7>31.44.
?? B
5????f(x)?logax(a>0?a?1)??f(x1x2x2014)?8??f(x21)
2
?f(x2)??f(x22014)????( )
A?4C?16
22
?? f(x1)?f(x2)??f(x22014) 22?logax1?logax22??logax2014
B?8 D?2loga8
?loga(x1x2x2014)2
?2loga(x1x2x2014)?28?16. ?? C
6?(log43?log83)(log32?log98)??( ) 5A.6 9C.4
25B.12D??????
?? (log43?log83)(log32?log98) 13?1???
????log3?log3log22?22323
23? ???25
12. ?? B
7??f(x)?log2x????[?1,1]????f(x)?????( )
?1??A.21????1?C.22???
B?[1,2]
?2?
D.?2? ?2?
1
?? ??1?log2x?12?x?2. ?? C
8???f(x)???????1?????????????y?ex??y?????f(x)?( )
A?ex?1C?e?x?1
B?ex?1 D?e?x?1
?? ???y?ex??y???????y?e?x???y?e?x
???????????????????f(x)?????f(x)?e?(x
?1)
?e?x?1. ?? D
9??f(x)?2x?2?xlga????????a?( ) 1A.3 1C.2
1B.4 1D.10
?? ?f(x)?????R????? ?f(0)?0??20?20lg a?0? 1?lg a??1??a10. ?? D
10?????????????????????????????????0.2????0.4 ????0.76??????????y??????x???????????( )
A?y?0.2x2x
C?y?10?? ????? ?? C ?????
12
B?y10(x?2x) D?y?0.2?log16x
11???y?ax?2?1(a>0??a?1)???????________? ?? (2,2)
lg?4?x?
12???y?________?
x?3
???4?x>0??x<4?
?? ????
???x?3?0??x?3?
?????{x|x<3?3<x<4}? ?? {x|x<3?3<x<4}
13???________.
?x2?1?x<0??
2f(x)??
?ex1 ?x?0??
?
?f(1)?f(a)?2??a?
2
?? 1??214?y?log0.3(x2?2x)???????________? ?? ?????????????? ?? (2???)
xa???x>1??
15????f(x)????R????????a?
4?2?x?2??x?1?????
?a??????________?
??4?a?
?? ?????2
a??a?4?22?
?? [4,8) ?????
16?(12?)?????? (1)(lg2)2?lg2lg50?lg25?
1
?7?0.5?10?3
(2)?2??2 ?2?0?
a>1?
?4?a<8.
?9??27?
1??6 1?log5?2?. (3)(lg5)?lg2lg5?lg20???4?125?22
2
4
?
?
? (1)(lg2)2?lg2lg50?lg25 ?(lg2)2?lg2(lg2?2lg5)?2lg5 ?2(lg2)2?2lg2lg5?2lg5 ?2lg2(lg2?lg5)?2lg5?2. (2)????9
??25?
?
11
?64?32
? ?? ?2
?27?
54
?332?3?2?1.
(3)???lg5(lg5?lg2)?lg20?25?25 ?lg5?lg2?1?2.
17?(12?)????f(x)?loga(1?x)?g(x)?loga(1?x)???a>0?a?1??h(x)?f(x)?g(x)?
(1)??h(x)??????????? (2)?f(3)?2???h(x)>0???x????
???????????1????????
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发表于 2019-9-13 23:46:11