dạng phương trình mũ logarit 2013

Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (1.2 MB, 12 trang )

BÀI GIẢNG PT - BPT - HPT Logarit và Mũ

Trần Quang Time goes, you say? Ah, no! Alas, time stays, we go

PHƯƠNG TRÌNH MŨ
: Đưa về cùng cơ số
1.
  

x x x
2
3 2 1
2 16

2.


2
x 6x 5/2
2 16 2

3.


2
x 4x
3 1 / 243

4.
5 17

73
32 0 25 128,.



xx
xx

5.
3
4 2 8 3
5 125
/xx


6.
21
48
xx


7.
x x 1 x 2
2 .3 .5 12



8.
2 9 27
3 8 64

   

   
   
xx

9.
 
x
x
x







2
1
1
3
2
2 2 4

10.
2
2 5 2 1
3 27
  


x x x

11.
1 2 1
4.9 3 2


xx

12.
3x 1 5x 8
(2 3) (2 3)

13.
x1
x1
x1
( 5 2) ( 5 2)

14.
1
3
3
1
( 10 3) ( 10 3)
x
x
x
x

15.
3
1 2 1 3
2 4 8 2 2 0 125. . . ,
  

x x x

16.
3
3
3
2 4 0 125 4 2, 
xx
x

17.
4
2
4
22
4
5 .0,2 125.0,04
x
x
x
xx
x







18.
4
1 2 3
2
5.4 2 16 3
x
xx


  

19.
2( 1)
1
2 3.2 7
x
x




20.
3 3 1 1
2 .3 2 .3 192
x x x x



21.
2
2 3 1
3
3 9 27 675
x
xx
  

22.
2 2 2 2
1 1 2
2 3 3 2
x x x x  
  

23.
22
3 9 9
4 16 16





x
x

24.
x
xx
2
21
( 1) 1

25.
23
3
3
1
9 27 81
3
x
x x x







26.
2 1 1
11
3.4 .9 6.4 .9
32
x x x x  
  

27.
  
  
x 4 x 3 x x 2
3 5 3 5

28.
   
  
x 1 x 2 x 4 x 3
7.3 5 3 5

29.
x x 1 x 2 x x 1 x 2
2 2 2 3 3 3
   
    

30.
 
3
2
9
2
2222
2


xxxx

x

31.
 
2
cos
1
2
cos
22 xx
x
x
x
x



: Đặt ẩn phụ.
1.
2 16 15 4 8 0  
xx

2.
9 8.3 7 0  
xx

3.

  

2x 8 x 5
3 4.3 27 0

4.
1 4 2
4 2 2 6
x x x  
  

5.
22
4 6.2 8 0
xx
  

6.
2
7
6.0,7 7
100
x
x
x


7.
13
3
64 2 12 0
xx


  

8.
22
2 1 2
4 5.2 6 0
x x x x    
  

9.
22
4 16 10.2
xx


10.
log log5
25 5 4.
x
x

11.
22
33
2log ( 16) log ( 16) 1
2 2 24
xx  


12.
22
12
9 10.3 1 0
x x x x   
  

13.
2x 6 x 7
2 2 17 0

  

14.




10
5 10
3 3 84
xx


15.
2 1 1
1
.4 21 13.4
2
xx



16.
3 2cos 1 cos
4 7.4 2 0
xx
  

17.
22
5 1 5
4 12 2 8 0.
    
  
x x x x

18.
3033
22

 xx

19.
x 1 3 x
5 5 26



20. D03
x x x x  


22
2
2 2 3

21.
22
sin cos
9 9 10
xx

22.
31
53
5.2 3.2 7 0
x
x


  

23.
12
5 5.0,2 26


xx

24.
1

4 4 3.2
x x x x


25.
22
sin cos
2 5.2 7
xx

26.
2
cos2 cos
4 4 3
xx


27.
1
5 5 4 0
xx

28.
2 2 2
2 1 2 2 1
9 34.15 25 0
     
  
x x x x x x

29.
1 1 1
x x x
2.4 6 9

www.VNMATH.com
BAỉI GIANG PT - BPT - HPT Logarit vaứ Muừ

Tran Quang Lost time is never found again

30.
1 1 1
6.9 13.6 6.4 0
x x x

31.
3 3 3
25 9 15 0
x x x

32.
A06
027.21812.48.3
xxxx

33.
07.714.92.2
22

xxx

34.
x x x
6.9 13.6 6.4 0

35.
27 12 2.8
x x x

36.
/2
4.3 9.2 5.6
x x x

37.
2 2 2
15.25 34.15 15.9 0
x x x

38.
25 12.2 6,25.0,16 0
x x x

39.
31
125 50 2

x x x

40.
xxx
27.2188

41.

2 3 2 3 14
xx

42.

2 3 2 3 2
xx

43.

4 15 4 15 8
xx

44.
xx
(2 3) (2 3) 4 0

45.
B07
( 2 1) ( 2 1) 2 2 0
xx

46.
( 3 2) (7 4 3)(2 3) 4(2 3)
xx

47.

02.75353
x
xx

48.
x x x 3
(3 5) 16(3 5) 2

49.

xx
(7 4 3) 3(2 3) 2 0

50.

26 15 3 2 7 4 3 2 2 3 1
x x x

51.

cos cos
5
7 4 3 7 4 3
2
xx

52.

7 3 5 7 3 5 14.2
xx
x

53.

xx
( 2 3) ( 2 3) 4

54.
xx
7 3 5 7 3 5
78
22

55.

10245245
xx

56.

3
7 5 21 5 21 2

xx
x

57.
xx
7 4 3 7 4 3 14

58.

10625625
tantan

xx

59.

xx
x

3
5 21 7 5 21 2

60.

sin sinxx
5 2 6 5 2 6 2

61.
3
31
81
2 6 2 1
22
xx
xx

62.
x x x x22
5
2 2 2 2 20
16

63.
11
3 3 9 9 6
x x x x

64.
x x x x1 3 2
8 8.0,5 6.2 125 24.0,5

65.

64)5125.(275.95
3

xxxx

66.
2
2 6 2 6
xx

67.
xxx
9133.4
13

68.
093.613.73.5
1112

xxxx

69.
24223
2212.32.4

xxxx

70.

2
2
1 2 1
4
2 3 2 3
23

x x x

71.
22
( 1) 2 1
101
(2 3) (2 3)
10(2 3 )

x x x

72.
3 1 2

2 7.2 7.2 2 0
x x x

S dng tớnh n iu ca hm s
1.
4 9 25
x x x

2.
x x x
3 4 5

3.
x
3 x 4 0

4.
x
x
4115

5.
2
2 2 2
3 2 2
xx
xx

6.
/2
2 3 1
xx

7.
x x x
3.16 2.8 5.36

8.
x
xxx
202459

9.

1/
52
2,9
25
xx

10.

2 3 2 3 2
xx
x

11.

3 2 3 2 10( ) ( )
x
xx

12.

xxx
5.22357

13.

xx
xx 2.1.24
2
2

14.
x
x
6
217.9

15.
32
1 1 1
5 4 3 2 2 5 7 17
2 3 6
x x x x
x x x
x x x

16.

2
4 2 2
3 ( 4)3 1 0
xx
x

17.

3 .2 3 2 1
xx
xx

18.
1 1 5
3 5 3 10
3 4 12
x x x
xx
x

19.
1 1 1
3 2 2 6
3 2 6
x x x
xx
x

20.
2013 2015 2.2014
x x x

www.VNMATH.com
BÀI GIẢNG PT - BPT - HPT Logarit và Mũ

Trần Quang Time goes, you say? Ah, no! Alas, time stays, we go

4:
Đưa về phương trình tích và Đặt ẩn phụ
khơng tồn phần.
1.
xxx
6132 

2. 8.3
x
+ 3.2
x
= 24 + 6
x

3.
2 1 1
5 7 175 35 0
x x x
   

4. D06
0422.42
2

22

 xxxxx

5.
22
2 ( 4 2) 4 4 4 8
x
x x x x      

6.
2 1 2
4 .3 3 2 .3 2 6
x x x
x x x x

    

7.
20515.33.12
1

xxx

8.
2 2 2
3 2 6 5 2 3 7
4 4 4 1
     
  

x x x x x x

9.
 
02.93.923
2

xxxx

10.
   
021.2.23
2

xx
xx

11.
 
0523.2.29  xx
xx

12.
 
035.10325.3
22


xx
xx

13.
 
1224
2
22
11

 xxxx

14.
22
2 1 2 2
2 9.2 2 0
x x x x  
  

15.
2 2 2
.2 8 2 2
xx
xx

  

16.
2 2 2 2
.6 6 .6 6
x x x x
xx

  
  

17.
3 2 3 4
2 1 2 1
.2 2 .2 2
xx
xx
xx
   

  

18.
 
9 2 2 .3 2 5 0
xx
xx    

19.
   
xx
xx    
2
3 2 2 1 2 0

20.
3.4 (3 10)2 3 0
xx

xx

21.
22
3.16 (3 10)4 3 0
xx
xx

    

22. ►
2 3 1 3
4 2 2 16 0
x x x
   

23. ►
x x x x
    
4 1 3 2 1
5 25.5 26.5 5 5 0

24. ►
x x x x
    
1
81 4.27 10.9 4.3 3 0

 Lơgarit hóa

6:
Hàm đặc trưng và PP đánh giá.
1.
2112212
532532


xxxxxx

2.
2
22
1 1 2
2
22
2

xx
xx
x
x

3.
1
2 4 1
xx
x

  

4.
 
2
11
124
2


x
xx

5.
x
xxxx
3cos.722
322
cos.4cos.3




6.
   
134732
1


x
xx

7.
x
x21

8.
x
x3 2 1

9.
x
x




1
1
22

10.
123223
1122


x
xxx
xx

11.
 
x
x
x


1
2cos
22
2

12.
x
x
2cos3
2


13.

2
cos 2
33
x
x

14.
4
2
16 2 2
xx
x

  

15.
2
3
2 6 9
4
x
xx

   



16.
2
2

1
2
xx
x
x



17.
4 6 25 2
xx
x  

18.
3 5 6 2  
xx
x

19.
xx
x  3 2 3 2

20.
xx
x   
2
3 2 3 2

21.

2 2 2
2 3 4 3
x x x
  

22.
2 2 2 2 2
1
2 3 7 8 4
x x x x x
   

23.
2 2 2
2 4.10 7 3
x x x
  

24.
8.3 3.2 24 6
x x x
  

PHƯƠNG TRÌNH LOGARIT
: Đưa về cùng cơ số
1.
2
log (5 1) 4x 

2.
2
5
log ( 2 65) 2
x
xx

  

3.
2
2
log 1
xx
x



4.
2
2 1/2
log ( 1) log (x 1)x   

9.
4 1 3 2
21
57
xx
   


   
   

10.
32
23
xx


11.
2
5 6 3
52
x x x

12.
2
5 .3 1
xx


13.
231224
3.23.2


xxxx

14.
3

2
3 .2 6
x
x
x


15.
1
2 .5 10
x
x
x

16.
22
3 2 6 2 5
2 3 3 2
x x x x x x    
  

1.
1
5 . 8 100
xx
x


2.

2
2 .3 9
xx

3.
2
2
8 36.3
x
x
x

4.
1 2 1
4.9 3 2
xx


5.
2
2
2 .3 1,5
x x x


6.
21
1
5 .2 50
x

x
x




7.
43
34
xx

8.
75
57
xx


www.VNMATH.com
BAỉI GIANG PT - BPT - HPT Logarit vaứ Muừ

Tran Quang Lost time is never found again

5.
55
log ( 3) log ( 2 6)xx

6.

log
2
3
1
3 1 2
2
x
xx

7.

22
log 6 log 3 1xx

8.
4 15
2
22
2
2
log 36
log 81 log 3
log 4
xx

9.
3 9 27
log log log 11x x x

10.
33
log log ( 2) 1xx

11.
93
log ( 8) log ( 26) 2 0xx

12.
2
22
log ( 3) log (6 10) 1 0xx

13.
32
1
log( 1) log( 2 1) log
2
x x x x

14.
3
4 1/16 8
log log log 5x x x

15.
3
22
log (1 1) 3log 40 0xx

16.
2
5
5
log (4 6) log (2 2) 2
xx

17.
34
1/3 3
3
log log log 3 3x x x

18.
2
5 0,2 5 0,04
log ( 1) log 5 log ( 2) 2log ( 2)x x x

19.
2 3 3
1/4 0,25 1/4
3
log ( 2) 3 log (4 ) log ( 6)
2

x x x

20.
3
loglog log(log 2) 0xx

21.
2
log 1 3log 1 2 log 1x x x

22.
42
log ( 3) log ( 7) 2 0xx

23.
21
8
log ( 2) 6log 3 5 2xx

24.
3
18
2
2
log 1 log (3 ) log ( 1)x x x

25.

21
2

2log 2 2 log 9 1 1xx

26.
4
log ( 2).log 2 1
x
x

27.
2
9
log 27.log 4
x
x x x

28.
22
33
log ( ) log ( ) 3xx
xx

29.
22
2 2 2
log ( 3 2) log ( 7 12) 3 log 3x x x x

30.
2
9 3 3

2log log .log ( 2 1 1)x x x

31.
5 3 5 9
log log log 3.log 225xx

32.

2
3
3
log 1 log 2 1 2xx

33.
23
48
2
log ( 1) 2 log 4 log ( 4)x x x

34.
2 2 2
2 3 2 3
log ( 1 ) log ( 1 ) 0x x x x

35.
22
93
3

11
log ( 5 6) log log 3
22
x
x x x

36.
42
21
11
log ( 1) log 2
log 4 2
x
xx

37.
2
22
5
log log ( 25) 0
5
x
x
x

38.

5
log 5 4 1
x
x

39.

44
2
log 2 ( 3) log 2
3
x
xx
x

40.

23
48
2
log 1 2 log 4 log 4x x x

41.

2
66
11
1 log log 1
72
x
x
x

42.

2
3
1
log 3 1 2
2
x
xx

43.
2
33

2log ( 2) log ( 4) 0xx

44.
log9 log
96
x
x

45.
5
5 50
log log

x
x

46.

2
log
1
log 6 5
x
x

47.
3
16

3 log 9
log
x
x
xx

48.

2
22
log 10 1 log4
log2
log (3 2) 2 log 5
xx
x

49.

2
log 9 2
1
3
x

x

50.
log ( ) log ( )
xx
x

1
4 4 2 3
21
2

51.
2
2 1 2
2
1
log ( 1) log ( 4) log (3 )
2
x x x

52. D07
22
1
log (4 15.2 27) 2log 0
4.2 3

xx
x

53.
8
42
2
11
log ( 3) log ( 1) log (4 )
24
x x x

54.

4
1
log 3 2 2 log16 log 4
42
xx
x

55.
1
1
2log2 1 log3 log 3 27 0
2

x
x

56.

3
22
log 4 1 log 2 6
xx
x

www.VNMATH.com
BAỉI GIANG PT - BPT - HPT Logarit vaứ Muừ

Tran Quang Time goes, you say? Ah, no! Alas, time stays, we go

57.

2
1
4
log 1 7 2.
1
21
21
xx
x
x

58.

4 3 2 3
1
log 2 log 1 log 1 3log
2
x

59.

22
22
4 2 4 2
22
log x x 1 log x x 1
log x x 1 log x x 1

60.
5
1
2log( 1) logx log
2
xx

61.
2
22
log ( 3) log (6 10) 1 0.xx

62.
2
1
log( 10) logx 2 lg4
2
x

63.
22
33

log ( 2) log 4 4 9x x x

64.

39
3
4
2 log log 3 1
1 log
x
x
x

65.
22
3
1
log (3 1) 2 log ( 1)
log 2
x
xx

66.

22
log (2 4) log 2 12 3

xx
x

: t n ph.
1.
23
log log 2 0xx

2.
2
22
log 2log 2 0xx

3.
22
3 log log (8 ) 3 0xx

4.

2 4 2
1
2 log 1 log log 0
4
xx

5.
1
33
log (3 1).log (3 3) 6

xx

6.
1
5 25
log (5 1).log (5 5) 1
xx

7.
3
3
22
4
log log
3
xx

8.
4 2 2 3
log ( 1) log ( 1) 25xx

9.
9
4log log 3 3
x
x

10.

( 1) 2
log 16 log ( 1)
x
x

11.
21
1 log ( 1) log 4
x
x

12.
2
2
log 16 log 64 3
x
x

13.
22
3
log (3 ).log 3 1
x
x

14.
2
2
log (2 ) log 2
x
x
xx

15.
2
55
5
log log ( ) 1
x
x
x

16.
2
2
log 2 2log 4 log 8
xx
x

17.
2

2
3
27
16log 3log 0
x
x
xx

18.

2
2
1/2 2
log 4 log 8
8
x
x

19.
23
/2 4 2
4 log 2log 3log
x x x
x x x

20.
2
3/ 3
log 2 log 1
x

x

21.
16 2
3log 16 4log 2log
x
xx

22.
23
/2 4 16
log 40log 14log 0
x x x
x x x

23.
22
1 2 1 3
log (6 5 1) log (4 4 1) 2 0
xx
x x x x

24.
22
3 7 2 3
log (9 12 4 ) log (6 23 21) 4
xx
x x x x

25.
A08
22
2 1 1
log (2 1) log (2 1) 4
xx
x x x

26.
2
log(10 ) log log(100 )
4 6 2.3
x x x

27.
2
2 2 2
log 2 log 6 log 4
4 2.3
xx
x

28.
2/ 2

log 2 log 4 3
x
x

29.
22
2
log 4 .log 12
x
xx

30.
24
log 4 log 5 0xx

31.
22
33
log log 1 5 0xx

32.
33
log 3 log log 3 log 1/ 2
x
x
xx

33.
44
4

2 2 2
log 2 log 2 log log
2
x
x
x x x

34.
33
log . log 3 3 log 3 3 6
x
x

35.
4 2 2 4
log log log log 2xx

36.
8
2
3log
log
2 2 5 0

x
x
xx

37.

12
1
4 log 2 logxx

38.
2
1 log( 1) 2
2
1 log( 1)
1 log ( 1)
x
x
x

39.
24
1 log 4 log 2 4xx

40.

2
22
log ( 1) 6log 1 2 0xx

S dng tớnh n iu ca hm s
1.
5
log ( 3) 4xx

2.
3
log ( 3) 8xx

3.
0,5
11
log
42
xx

4.

2
22
log (x x 6) x log (x 2) 4

www.VNMATH.com
BÀI GIẢNG PT - BPT - HPT Logarit và Mũ


Trần Quang Lost time is never found again

5.
2
log( 12) log( 3) 5x x x x     

6.
2
log
2.3 3
x
x 

10 .
   
23
log 2 1 log 4 2 2
xx
   

11.
   
32
log 2 log 3 2xx   

12.
35
log ( 1) log (2 1) 2xx   

13.
   
32
4( 2) log 2 log 3 15( 1)x x x x     



x
xx



2
2 log ( 2)
6
21

 :
 
2
4 4 1 1
x
x 
có đúng 3
nghiệm thực phân biệt.

4:

Phương trình tích và đặt ẩn phụ khơng
tồn phần.
1.
0)(log).211(
2
2
 xxxx

2.
xxxx 26log)1(log
2
2
2


3.
 
112log.loglog2
33
2
9
 xxx

4.
6 3 2 2 2
2 2 2 2
1
log (3 4) .log 8log log (3 2)
3
x x x x   

5.
       
2
33
3 log 2 4 2 log 2 16x x x x     

6.
2 3 2 3
log .log 1 log logx x x x  

7.
2 3 2 3
log .log log logx x x x

8.
2 2 2
4 5 20
log ( 1).log ( 1) log ( 1)x x x x x x      

9.
2
22
log ( 3).log 2 0x x x x    

10.
2
33
(log 3) 4 log 0x x x x    

11.
3logloglog.log
2
3
332
 xxxx

12.
       
0161log141log2
3
2
3
 xxxx

13.
     
0621log51log
3
2
3
 xxxx

14.
       
2 2 2 2 2
1 log 1 4 2 1 .log 1 0x x x x     

15.
xxxx

7272
log.log2log2log 

16.
2
33
log ( 12)log 11 0x x x x    

17.
2
22
log 2( 1)log 4 0x x x x   

18.
2 3 5
2 3 2 5 3 5
log .log .log
log .log log .log log .log
x x x
x x x x x x  

19.
3
3 2 3 2
31
log .log log log
2
3
x
xx

x
  

20.
22
log log
2
(2 2) (2 2) 1
xx
xx    

21.
 
2 2 2 2
6 1/6
.log 5 2 3 log 5 2 3 2x x x x x x x x      

22.
3
2 3 3 2
log .log log log 3x x x x

23.
     
22
2 1 1 2
3 .log 1 2 log 2 3 .log 2 2log 1
xx
x x x x


      

24.
   
2
2 7 7 2
log log 3 / 2 2 log 3 logx x x x x x

    


25.
   
1
4 2 2 2 1 sin 2 1 2 0
x x x x
y

      

5: Mũ hóa
1.


x x x
4
4
18
2log log

2.
 
xx
57
log2log 

3.
 
xx
32
log1log 

4.
22
32
log ( 2 1) log ( 2 )x x x x   

5.
32
2log tan log sinxx

6.
23
log log 1xx

7.
53
log log log15xx

8.
2 2 3 3
log log log logxx

9.
x x x
2 3 3 2 3 3
log log log log log log

10.
2 3 4 4 3 2
log log log log log logxx

11.
2 2 2
log 9 log log 3
2
.3
x
x x x

12.
3
2
3 log log
3
3
100. 10
xx

x

13.
x
x
x
log 5
5 log
3
10

14.
2
22
log 1 2log
2 224
xx
x



15.
2
log 3log 4,5 2log
10
x x x
x
  


16.
2 2 2
log log 3 3log
36
xx
x

17.
9
log
2
9.
x
xx

18.
2
log
22
2
2. log
2
x
x
xx

áp 6:
PP đánh giá và dùng hàm đặc trưng.
1.

2 2 3
22
1
log (2 ) log 3 2
2
x x x x   

2.
3
2
log 1
22
22
3 2 log ( 1) log
x
x x x

   

3.
22
55
2 log ( 4) logx x x x x    

4.
2 2 2
ln( 1) ln(2 1)x x x x x     

www.VNMATH.com
BAỉI GIANG PT - BPT - HPT Logarit vaứ Muừ

Tran Quang Time goes, you say? Ah, no! Alas, time stays, we go

5.
2
2
2
2
1
log 3 2
2 4 3
xx
xx
xx

6.
11
1
37
log 30 3 3.7
4.7 30
xx
xx
x

7.
2
2
2015
2
3
log 3 2
2 4 5
xx
xx
xx

8.
2
2
3
2
3
log 7 21 14
2 4 5
xx
xx
xx

9.
2
1
12
22
2 .log ( 1) 4 .(log 1 1)
x
x
xx

10.
sin( )
4
tan

x
ex

11.
2 1 3 2

2
3
8
22
log (4 4 4)
xx
xx

12.

23
1
log 2 4 log 8
1
x
x

13.
2
21
log 1 2
x

x
x
x

14.
log 1 lg 4,5 0
x
x

A02: Cho phng trỡnh
22
33
log log 1 2 1 0x x m
(1) (m l
tham s)
a) Gii phng trỡnh (1) khi m = 2.
b) Tỡm m phng trỡnh (1) cú ớt nht
mt nghim thuc on
3
1 ; 3

.

www.VNMATH.com
BÀI GIẢNG PT - BPT - HPT Logarit và Mũ


Trần Quang Lost time is never found again

BẤT PHƯƠNG TRÌNH MŨ
1.
2
2
3 27
xx


2.
15
2
log
3


x
x

3.
1
1
1
( 5 2) ( 5 2)
x
x
x




  

4.
2
2 16
11
( ) ( )
39
x x x


5.
1
2
1
1
2
16
x
x







6.
1 2 1 2
2 2 2 3 3 3
x x x x x x   
    

7.
2 2 2
3 2 3 3 3 4
2 .3 .5 12
x x x x x x     


8.
31
13
( 10 3) ( 10 3)
xx
xx


  

9.
2
1 3 9
xx


10.

2
2
56
11
3
3
x
xx




11.
 
2
27
21
xx
x



12.
11
2 2 3 3
x x x x
  

13.
1

1
( 2 1) ( 2 1)
x
x
x


  

14.
2
1
2
1
3
3
xx
xx







15.
9 2.3 3 0
xx
  

16.
2 6 7
2 2 17 0
xx
  

17.
3
2 2 9
xx


18.
2.49 7.4 9.14
x x x


19.
5.2 7. 10 2.5
x x x


20.
1
4 3.2 4
x x x x


21.
2 2 2

2 2 2
6.9 13.6 6.4 0
x x x x x x  
  

22.
2 1 2
4 .3 3 2 .3 2 6
x x x
x x x x

    

23.
2
8.3 2
1
3 2 3
x
x
xx







24.
922

7

xx

25.
12
3
1
3
3
1
1
12















xx

26.
4loglog
.3416
aa
x
x


27.
   
xx
xx
xx 



2
2
2
153215
1

28.
09.93.83
442

 xxxx

29.
 

13.43
224
2

 xx
x

30.
8log.2164
4
1

 xx

31.
 
 
52824
3
12
12



x
xx

32.
02
2

1
212
32
12










x
x

33.
1 1 1
9.4 5.6 4.9
x x x
  


34.
xxxx
993.8
1
44




35.
 
11
2

x
xx

36.
2 2 2
2 2 2
6.9 13.6 6.4 0
x x x x x x  
  

37.
xx
xxxxxxx 3.43523.22352
222


38.
62.3.23.34
212


xxxx
xxx

39.
   
1
1
1
1525




x
x
x

40.
222
21212
15.34925
xxxxxx 


41.
 
105
5
2
5
log
log


x
x
x

42.
 
 
 
12log
log
1
1
3
35
12,0










x
x
x
x

43.
 
13.43
224
2

 xx
x

44.
 
15
9log33loglog
3
3
log.2
2
2
1

 x
x

45.
126
6
2
6
loglog


xx
x

46.
   
125.3.2
2log1loglog
222

 xxx

47.
23.79
1212
22

 xxxxx

48.
32
4log
2

x
x

49.
1282.2.32.4
222

212


xxxx
xxx

50.
01223
2
121


x
xx

BẤT PHƯƠNG TRÌNH LOGARIT

1.
2
1
18
log
2
2



x
xx

2.
 
123log
2
2
1
 xx

3.
   
243log1243log
2
3
2
9
 xxxx

4.
3
1
6
5
log
3



x
x

x

5.
2
1
1
12
log
4



x
x

6.
2
4
1
log 






x
x

7.

x
x
x
x
2
2
1
2
2
3
2
2
1
4
2
log.4
32
log9
8
loglog 


















www.VNMATH.com
BAỉI GIANG PT - BPT - HPT Logarit vaứ Muừ

Tran Quang Time goes, you say? Ah, no! Alas, time stays, we go

8.

xxxxx 2log1244log2
2
1
2
2

9.

154log
2
x
x

10.

48loglog
22

x
x

11.

01628
1
5
log134
2
5
2
xx
x
x
xx

12.

03log7164
3
2
xxx

13.

3log
2
1
2log65log
3
1
3
1
2
3
xxxx

14.
1
1
32
log
3

x
x

15.
xxxx
3232

log.log1loglog

16.

1log
1
132log
1
3
1
2
3
1

x
xx

17.

23log
2
2
xx

18.

24311log
2

5
xx

19.

264log
2
2
1
xx

20.

xx 2log1log
2
2
1

21.

1log
12
96
log
2
2
2
1

x
x
xx

22.

1
8
218
log.218log
24

x
x

23.

193loglog
9

x
x

24.

15log1log1log
3
3
1
3
1
xxx

25.

13log
2
3

x
xx

26.

12log
2
xx
x

27.

x
xx
x
xx
x
2
log2242141
2
1272
22

28.

2385log
2
xx

x

29.
22
32
log ( 2 1) log ( 2 )x x x x

30.

4
3
16
13
log.13log
4
14

x
x

31.

015log
3,0
xx

32.

0
352
114log114log
2
3
2
11
2
2
5

xx
xxx

33.

2
3
2
9

4
1
loglog

xx

34.
2
1
2
54
log
2

x

x
x

35.

3
2
1
2
1
21log1log
2
1
xx

36.
1log
2
1
log
2
3
2
3
4
xx

37.

0
14log
5
2

x
x

38.

22log1log
2
2
2
xx

39.

x
x
x
2log1
12
6
2

40.

0
82
1log
2
2
1

xx
x

41.
xx
8
1
2
8
1
log41log.91

42.

164loglog
2

x
x

43.
xxxx
5353
log.logloglog

44.

2
3log
89log
2
2
2

x
xx

45.

2log
1
log22log
2
2

x
x
x

46.
1
1
12
log

x
x
x

47.
1
log1
log1
3
2
3

x
x

48.
1log2log
4
3
4
3
2
xx

49.

3
5log
35log
5
3
5

x
x

50.
2

1
122log
2
1
2

xx
xx

51.
2log
2
1
log
7
7
xx

52.

0
43
1log1log
2
3
3
2
2

xx
xx

53.

2
2lglg
23lg
2

x
xx

54.

2
3
log 5 18 16 2
x
xx

55.
316log64log
2
2

x
x

56.
0loglog
2
4
1
2
2
1
xx

www.VNMATH.com
BAỉI GIANG PT - BPT - HPT Logarit vaứ Muừ

Tran Quang Lost time is never found again

57.

2log2log
12

xxx

58.

1log.
112
1

log1log.2
5
15
2
25

x
x
x

59.

232log1232log
2
2
2
4
xxxx

60.
x

x
x
x
2
2
1
2
2
3
2
2
1
4
2
log4
32
log9
8
loglog

61.

3log53loglog
2
4
2
2
1
2
2
xxx

62.

73log219log
1
2
1
1
2
1

xx

63.

33
log x log x 3 0

64.

2
14
3
log log x 5 0

65.

2
15
5
log x 6x 8 2 log x 4 0

66.

1x
3
5
log x log 3

2

67.

x 2x 2
log 2.log 2.log 4x 1

68.

22
log x 3 1 log x 1

69.

81
8
2
2 log (x 2) log (x 3)
3

70.

31
2
log log x 0

71.

5x
log 3x 4.log 5 1

72.

2
3
2
x 4x 3
log 0
x x 5

73.

13
2
log x log x 1

74.

2
2x
log x 5x 6 1

75.

2
2
3x
x1
5
log x x 1 0
2

76.

x 6 2
3
x1
log log 0
x2

77.

2
22
log x log x 0

78.

xx
2
16
1
log 2.log 2
log x 6

79.

2
3 3 3
log x 4 log x 9 2 log x 3

80.

24
1 2 16
2
log x 4log x 2 4 log x

81.

224log12log
32

xx

www.VNMATH.com
BÀI GIẢNG PT - BPT - HPT Logarit và Mũ

Trần Quang Time goes, you say? Ah, no! Alas, time stays, we go

HỆ PHƯƠNG TRÌNH MŨ - LOGARIT

I. Hệ phương trình mũ.
1.

















13
3
5
4
yx
yx
x
y
xy

2.
   








yxyx
x
y
y
x
33
log1log
324

3.










4
23
99.
3
1
2
1
y
x
x
yx
y
x
y

4.
 









y
y
y
x
x
y
y
x
12
3
5
2
3.33
2.22

5.





2lglg
1

22
yx
xy

6.







723
7723
2
2
y
x
yx

7.








1932

63.22.3
11 yx
yx

8.










3
3
3
3.55
5
yx
yx
yx
yx

9.











y
yy
x
xx
x
22
24
452
1
23

10.
 
 









068

13.
4
4
4
4
yx
xy
yx
yx

11.
   







3lg4lg
lglg
34
43
yx
yx

12.
 









1log
.
3log
4
2
5
log
xy
y
x
y
y
xxy

13.








113

2.322
2
3213
xxyx
xyyx

14.
   
   







421223
421223
xy
yx

15.










xy
3x 2y 3
4 128
51

16.









2
xy
(x y) 1
5 125
41

17.








2x y
xy
3 2 77
3 2 7

18.







xy
2 2 12
x y 5

19.
32
1
2 5 4
42
22
x
xx
x
yy
y











1
32
3 9 18
y
y
x
x









20.
21.
22
1
22
x y x

x y y x
xy


  


  



22.
21
21
2 2 3 1
2 2 3 1
y
x
x x x
y y y



    


    



II.Hệ phương trình lơgarit
1)
  





16
2loglog
33
22
yx
xyxyyx

2)
   







3lg4lg
lglg
34
43
yx
yx

3)
 





1log
3log2loglog
7
222
yx
yx

4)
 





8
5loglog2
xy
yx
xy

5)






1loglog
4
44
loglog
88
yx
yx
xy

6)





1loglog
4
44
loglog
88
yx
yx
xy

7)
 









1log
43
3.11
3
yx
x
x
x
y

8)
   
   





xx
yx
4224
2442

loglogloglog
loglogloglog

9)
 
   








3
8
1log2log
142
21
xy
yxyx
yx

10)
 
 






223log
223log
xy
yx
y
x

11)
   
   







453log.53log
453log53log
xyyx
xyyx
yx
yx

www.VNMATH.com
BAỉI GIANG PT - BPT - HPT Logarit vaứ Muừ

Tran Quang Lost time is never found again