Chuyên đề MŨ và LOGARIT TUYỆT ĐỈNH

PHÂN LOI PHƯƠNG TRNH LOGARIT THEO PHƯƠNG PHP GII
PHÂN LOAI BÀI TẬP PHƯƠNG TRNH LÔGARIT
I.Phương trình cơ bản



 
  
= ⇔ =



     
= ⇔ =


 
   
    
  
> >

= ⇔

=


II.Một số phương pháp giải phương trình lôgarit
Phương pháp 1 !"#
$%&'()*+,!)-./
 

    =
0*12=





3

=


1.
xx
3322
loglogloglog =
2.
xx
234432
loglogloglogloglog =
3.
xxx
332332
loglogloglogloglog =+
4.
5.
6.
7.
8.
9. "45

10.
11. "445/
12.
13.
14.
+
+ = − −
x x 1
log (4 4) x log (2 3)
2 1
2

15.
67
8

8
8

8
8
xxx −=++−
16.
17.
18.
19.
( )
7
8
5

7

886
7
x
xx
−+=−
−

20.
8966
8

88

=








+−







++
x
x
21.
( ) ( )
587
6
88
−+=+
+xx
x

22.
( )
( )
8
7

89
8
8

xx
x
x
−+
−=
−

23.
( )
[ ]
{ }
8

68
6867
=++ x
24.
( )
88
66
8
:
−+= xxx
25.
(
)
8

86
8
6
=+−−
+
xx
x
26.
( ) ( )

6
;
8
8
7
778 xxx ++−=++
27.
( ) ( ) ( ) ( )

87
8
87
8
8
8
8
8
+−+++=+−+++ xxxxxxxx
28.
( )
( )
8
:
6
6
8
89
6
8
6


8

5< −+
−
=+− x
x
xx
29.
;
7 8
8
 
  6     7 
8 7
x x x+ + − =
30.
6
6 8 6 8
6 
   
8
6
x
x x
x
− = +
31.
<


8   
8
x x− = −
32.
8
8 8
  6  5   
2 6
x x
DK x
− − − + =
>
33.
8

   8 7
8
+ + = −x
34.
8 8 6
8 8

 8   6 8
8
x x x x+ − = −
35.
6
8
 8 8
8 8

6 8    
x
x x x
+
− = + −
36.
8 8
6 6
  8  7 7 :x x x+ + + + =
=248<4>8:
37.
7
  8 8 
x
x + =
38.
8 8
8 8 8
  6 8   9 8 6  6x x x x+ + + + + = +
39. (Chưa gii đưc)
40.
41.
42.
43.
788
8
66
=−+− xx
44. 
8

8
8
=−−++− xxxx

45.
2 3
4 8
2
log (x 1) 2 log 4 x log (4 x)+ + = − + +
46.
xxxx 85
8
8
8
−=−+
? @,A&B&,!)-CD
( )
xxx
7
7
5
8 =+
( )
xx
<9
8 =+
( )
xx
68
 =+

8 8
6 8
  8    8 x x x x+ + = +
Phương pháp 2? @,A&B&,!)-&/"#
EF1C#GHIJ)(IBFKGL,
( ) ( )
<<<

8<<
=−−
+xx
  8
 5   
x
x
+
= +
8 8
8
 7  8
x
x x =
8 7
 7  < x x− − =

 

   

  

            
  
= ⇒ = = = =
M(N
3
3
2 2
4
log x log x
3
+ =

<
8
6
8
6
=−++ xx
Phương pháp3,!)-OPQRSTCU,!)-!V,!)-
V&LWIIXIJX,V. @,A&B&!VBFK)MXIR
S
2 7 2 7
log x 2. log x 2 log x.log x+ = +
Phương pháp 4=S.AO&!&FYTC"#
3,!)-./=C
Z@CC


0KC&[%\%⇒


TC.F]^
3,!)-./=
Z@CC


0KC&[%_\%\%_&[%
⇒

TC.F]^
3./F=
0KC&[%\%⇒,!)-⇔F=
3,!)-=
Z@C&LC


8

0KCGA(``N⇒`&[%%⇒`=
XJaFICUC⇒=XJaFIC⇒,C


8
1.
( )
8
8 8
   5 8x x x x+ − = −
2.
2
2 2

log (x x 6) x log (x 2) 4− − + = + +
3.
4.
5.
 
6.
7.
( )
( )
8
 5 7  8x x x x+ − − = + +
8.
( ) ( ) ( ) ( )
8
6 6
6  8 7 8  8 5x x x x+ + + + + =
9.
789
<78
6

8
8
8
6
++=









++
++
xx
xx
xx
10.
6 6
6    x x− − =
11.
8
8 8
   8 5 x x x x+ − + − =
12.
8

 8
8 8
8    7   
x
x
x x
+
+
+ = + +
13.
Phương pháp 5II

,!)-%./b=c
0CbdPceP]bePcdP
c!)-⇔b=c=PfKV])