Bài tập tổng hợp phương trình mũ hay, khó qua các năm. có đáp án

ph ơng trình và bất ph ơng trình mũ
i) ph ơng pháp logarithoá và đ a về cùng cơ số
1)
5008.5
1
=

x
x
x
ĐHKTQD - 98
2)
( ) ( )
244242
22
1
+=+ xxxx
x
ĐH Mở - D - 2000
3)






+
xx
xx
2
2

2
,,
4)
( ) ( )




+
+ 22
!"
5)



=
+ 34x
#$!% !"
6)
( ) ( )
3
1
1
3
310310
+
+


<+

x
x
x
x
ĐHGT - 98
7)
24
52
2

=
xx
8)
1
2
2
2
1
2



x
xx
9)
2121
444999
++++
++<++
xxxxxx

10)
13
12
2
1
2
1
+
+

x
x
11)
( )
112
1
1
2
+
+

x
x
xx
12)
( )
3
2
2
2

11
2
>
+
xx
xx
13)
2431
5353.7
++++
++
xxxx
Ii) Đặt ẩn phụ:
1)
1444
7325623
222
+=+
+++++ xxxxxx
HVQHQT - D - 99
2)
( ) ( )
4347347
sinsin
=++
xx
ĐHL - 98
3)
( )
1

2
12
2
1
2.62
13
3
=+
xx
xx
ĐHY HN - 2000
4)
( )
05232.29 =++ xx
xx
ĐHTM - 95
5)
( )
77,0.6
100
7
2
+=
x
x
x
ĐHAN - D - 2000
6)
1
12

3
1
3
3
1
+






+






xx
= 12 HVCTQG TPHCM - 2000
7)

>






+






+1
&
8)
1099
22
cossin
=+
xx
ĐHAN - D - 99
9)
1 1 2
4 2 2 12
x x x+ + +

+ = +
ĐHTCKT - 99
10)
2 2
2 1 2 2
2 9.2 2 0
x x x x+ + +
+ =
ĐHTL - 2000
11)
( ) ( )( ) ( )
3243234732 +=+++
xx
ĐHNN - 98
12)
'(

=++
+
9
#)*%
13)
'+'',

=+
"/01- i
Trang: 1
14)
+


<
234*5
15)
( ) ( )





≤−++
+
( )
 
16)


=+
+
26
17)


+=

27701-!
18)
( ) ( )
''

=++

8*729
19)
',

=+
+

26:;01-!
20)
0173.
3
26
9 =+






−
xx

2 "/01-! i
21)
09.93.83
442
>−−
+++ xxxx
§HGT - 98
22)

022
64312
=−
−++ xx
23)
( ) ( )
43232 =++−
xx
24)
( ) ( )
02323347 =+−−+
xx
25)
111
222
964.2
+++
=+
xxx
26)
12.222
56165
22
+=+
−−+− xxxx
27)
101616
22
cossin
=+

xx
28)
0
12
122
1
≤
−
+−
−
x
xx
29)
xxxx
22.152
53632
<+
−+−−+
30)
222
22121
5.34925
xxxxxx −−+−+
≥+
31)
03.183
1
log
log
3

2
3
>+−
x
x
x
32)
09.93.83
442
>−−
+++ xxxx
33)
3log
2
1
1
2
4
9
1
3
1
>






−







− xx
34)
9339
2
−>−
+ xxx
35)
xxxx
993.8
44
1
>+
++
36)
1313
22
3.2839
−−+−
<+
xx
37)
013.43.4
21
2

≤+−
+ xxx
38)
2
5
2
2
1
2
2
1
log
log
>+
x
x
x
39)
0124
21
2
≤+−
+++ xxx
III) ph ¬ng ph¸p hµm sè:
1)
12
21025
+
=+
xxx

HVNH - D - 98
2)
xxx
9.36.24 =−
§HVL - 98
3)
2
6.52.93.4
x
xx
=−
§HHH - 99
4)
13
250125
+
=+
xxx
§HQG - B - 98
5)
( )


1
2
1
−=
−−
x
xxx

0<=
6)
( )




++−>++−
2525 xx
x

/4& i
7)
163.32.2 −>+
xxx
§HY - 99
8)
x
x
381
2
=+
9)
5loglog2
22
3 xx
x
=+
10)
( )

0331033
232
=−+−+
−−
xx
xx
11)
( )
2
1
122
2
−=+−
−−
x
xxx

12)
1323
424
>+
++ xx
13)
0
24
233
2
≥
−
−+

−
x
x
x
14) 3
x
+ 5
x
= 6x + 2
Trang: 2
Mét sè bµi to¸n tù luyÖn:
1) 3
x+1
+ 3
x-2
- 3
x-3
+ 3
x-4
= 750 2) 7. 3
x+1
- 5
x+2
= 3
x+4
- 5
x+3

3) 6. 4
x

- 13.6
x
+ 6.9
x
= 0 4) 7
6-x
= x + 2
5)
( ) ( )
43232 =++−
xx
(§Ò 52/III
1
) 6)
132
2
+=
x
x
(§Ò 70/II
2
)
7) 3 25
x-2
+ (3x - 10)5
x-2
+ 3 - x = 0 (§Ò 110/I
2
) 8)
( ) ( )

x
xx
23232 =−++
9)5
x
+ 5
x +1
+ 5
x + 2
= 3
x
+ 3
x + 3
- 3
x +1 1
( )
( ) ( ) ( )
2121
2
5
6
318
12
2
143
3
333222202162194218
41151710245245160466139615
04551433681242111110
2

2
2
−−−−
+−
−+−
−−
+
−−+
−
+−=++==
=+=−++=+−
=+−===+
xxxxxx
xx
xxx
x
xxx
xxx
xxx
x
x
xxx
x
x




( )
( )
( )
01722)260273.43)25122)24
1)2311)22125.3.2)21
7625284
4
2
2
2
1
221
2
2
=−+=+−=+−
=−=+−=
++++
−
−
−
−−
xxxx
x
x
x
xxx
xx
xxxx



( ) ( )
084.1516.2)28043232)27 =−−=−−++
xx
xx

( ) ( ) ( ) ( )
3
2531653)3002323347)29
+
=−++=+−−+
x
xxxx

012283396423236581216331
332111
=+−=+=+
+
x
x
xxxx
xxx

( ) ( )
( )
( )
( )


(




,





>,?,
'>,,+
?


?


==
==
=






=−+−−
++=++=−+=+
−−
−
−

+
+
+
++
+
+++−
33
3
1
13
1
10
3
3
1
122
2112212
25,0
125,0.4
021223)37
532532)36043)35543)34
x
x
x
x
x
x
xx
xxxxxxxxxx
xx

x
xx
11
211
12
50.25,425 =+=
=






=






+−−
−






,'>,
,,


(
+

>',


024-10.2-4 48) 0336.3- 947)
1-xxxx
22
==+
−− 31
@AB51CDEA
!

  ?  
 ,
− + −
=
/


 '

 ' 
− −
=
*
         
     

− − − −
+ + = − +
-
    
   
− −
=
F

  
   
−
− + =
G
  
    
−
− =


 , 
   
−
− + =
@AB51CDEA
!
, ?  
 , ( 
+ +
− + =

/
 '  (
  ( 
+ +
+ − =
*
 
    , + + − − =
-
 
' , ? − − =
F
   
  '  
+
+ + − =
G
 
( ,     + − − + =

  
' ? '+ =

  
  
, ' ++ =

  
 
?   

+
− + =
H
         
     
+ + + +
+ + = + +

 
  
−
+ =

@AB51CDEA
!
  
 , + =
/

  , + − =
*
  
       − − + − =
-
         
     
− + + +
+ + = + +
@,AB5*4*81CDEA
!

 I
 I 
, ?
 
+
− −

=


=


/

 I
 I 
 
, 
+
− −

=


=


/
 I

 I
  ((
  (

− =


− =


-
 I
  
 I 

+ =

+ =

F
 I  I

 ,
 I  I

 '
J J J J
   
− −
+ +


− = −



− = −

:KJ>L
@AB5:@/801CDEA
!
 
J  J J 
−
− + + =

/
 
J J ?
−
+ =
@'AEJJMN1CDE*O8JA
 
J ,+ J  J  − − − + − =
@(AB5*4*/P1CDE3!A
!
'

 
+ 
+

<
/


 
 
 
−
+
≥
*

 
  
−
< <
-
 
   − + <
F
 

 
   
−
+
+ + <
G



   
   
+
− > −

@?AB5*4*/P1CDE3!A
!
 
 +  
−
+ − <
/
  
,  ( + − ≤
*
  
 
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+
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+ −
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, J  
−
− + >
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+ >
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   
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( )
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− + + = +
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− = −
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0"  0" I 
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− =
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I
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0" I 0" 
I ,I 
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=
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