Chuyên đề phơng trình Bất ph ơng trình và Hệ phơng trình mũ Loga rit
ph ơng trình và bất ph ơng trình mũ
i) ph ơng pháp logarit hoá và đ a về cùng cơ số
1)
5008.5
1
=

x
x
x

2)
( ) ( )
244242
22
1
+=+
xxxx
x

3)
1
3
2.3




+
xx


<+
x
x
x
x
7)
24
52
2

=
xx
8)
1
2
2
2
1
2



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

2
11
2
>
+
xx
xx
13)
2431
5353.7
++++
++
xxxx
Ii) Đặt ẩn phụ:
1)
1444
7325623
222
+=+
+++++
xxxxxx

2)
( ) ( )
4347347
sinsin
=++
xx
3)
( )

6)
1
12
3
1
3
3
1
+






+






xx
= 12
7)
12
3
1
3
3

4 2 2 12
x x x+ + +
+ = +
10)
2 2
2 1 2 2
2 9.2 2 0
x x x x+ + +
+ =
11)
( ) ( )( ) ( )
3243234732
+=+++
xx
12)
06.3-1-7.35.3
1xx1-x1-2x
=++
+
9
13)
06.913.6-6.4
xxx
=+
14)
32.3-9
xx
<
15)
0326.2-4

26
9
=+







xx
21)
2 4 4
3 8.3 9.9 0
x x x x
+ + +
=

22)
022
64312
=
++
xx
23)
( ) ( )
43232
=++
xx
24)


+

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



xx
34)
9339
2
>
+
xxx
35)
xxxx
993.8
44
1
>+
++
36)
1313
22
3.2839
+
<+
xx
37)
013.43.4
21
2
+
+
xxx

xxx
9.36.24
=
10)
( )
0331033
232
=++

xx
xx
1
Chuyªn ®Ò ph¬ng tr×nh BÊt ph– ¬ng tr×nh vµ HÖ ph¬ng tr×nh mò Loga rit –
3)
2
6.52.93.4
x
xx
=−
4)
13
250125
+
=+
xxx
5)
( )
2
2
1

11)
( )
2
1
122
2
−=+−
−−
x
xxx

12)
1323
424
>+
++
xx
13)
0
24
233
2
≥
−
−+
−
x
x
x
14) 3

2 3 1
x
x
= +
6) 3
x+1
+ 3
x-2
- 3
x-3
+ 3
x-4

= 750
7) 3..25
x-2
+ (3x - 10)5
x-2
+ 3 - x = 0
8)
( ) ( )
x
xx
23232
=−++
9)5
x
+ 5
x +1
+ 5

16) 5 24 5 24 10
x x x x x
x x
−
− + = − + =
+ + − =
( )
2
8 1 3
17) 15 1 4 18)2 4
x
x x x x− + −
+ = =
2
5
6
2
1 2 1 2
19)2 16 2
20)2 2 2 3 3 3
x x
x x x x x x
− +
− − − −
=
+ + = − +
( )
(
)
( )

28)2.16 15.4 8 0
x x
x x
( )
2 2
3
x 3 x 3 x-1
42) 2 .5 0,01. 10
− −
=
( ) ( )
+ − − + =29) 7 4 3 3 2 3 2 0
x x
( ) ( )
+
+ + − =
3
30) 3 5 16 3 5 2
x x
x
1 1 1
2 3 3
31)3.16 2.81 5.36
32)2.4 6 9
33)8 2 12 0
x x x
x x x
x
x x
+

2 x 1
4 x 10
3 1
x-3
3
1
3x-7
1
38) 3.3 . 81
3
39) 2 4 .0,125 4 2
40) 2.0,5 -16 0
41) 8 0,25 1
x
x
x
x
x
x
+ +
+
+
+
+
−
−
 
=
 ÷
 

47) 9 -36.3 3 0
48) 4 -10.2 -24 0
− −
+ =
=
hÖ ph ¬ng tr×nh mò vµ hÖ ph ¬ng tr×nh logarit
1)
( ) ( )
2 2
log 5 log
l g l g4
1
l g l g3
x y x y
o x o
o y o
− = − +


−

= −

−

20)
( ) ( )
1
l g 3 l g 5 0
4 4 8 8 0

3)





=
=
+−
5
1
10515
2
xy
y
xx
4)
( )



=+
=
+
323log
2log
1
y
y
x

3
3
1log
y
x
xy
7)
( )
2
4
4
9 27.3 0
1 1
l g l g lg 4
4 2
xy y
o x o y x

− =


+ = −


8)
( )





o x y o x y o

+ = +


+ − − =


11)
( )
( ) ( ) ( )



+=−−−−
=
−+
xyxyxy
xy
555
log21
loglog122log2
483
3
12)
( ) ( )
( )
yxyxyx
+=−=+
3

yx
xy
5
log3
27
5
3
21)
( )
( )



=+
=+
232log
223log
yx
yx
y
x
22)
( )





>=
+=




=−
=−
1log
1loglog
2
2
xy
x
x
y
yxy
25)
( ) ( )



=−
−=+
1loglog
22
yx
yxyx
yx
26)
( )





≠≠=
=
0pq vµ qp
y
x
y
x
yx
a
a
a
qp
log
log
log
29)





=







53
542
12
yx
yx
yx
yx
xyxy
16)
( ) ( )





>=
=
0x 642
2
2
y
y
x
x
17)






=
+−
0x 8
1
107
2
yx
x
yy
19)







=
=+










−

3 4
4 3
o x o y
o o
x y
=



=


36)
( )





<=+
=
0a
2222
2
lg5,2lglg ayx
axy
37)




xxyx
yx
xyx
yx
39)



=−
=+
1loglog
272
33
loglog
33
xy
yx
xy
PH¦¥NG TR×NH Vµ BÊT PH¦¥NG TR×NH LOgrIT
1.
( ) ( )
5 5 5
log x log x 6 log x 2= + − +
2.
5 25 0,2
log x log x log 3+ =
3.
( )
2
x

x 16 2
3log 16 4 log x 2 log x− =
10.
2
2x
x
log 16 log 64 3+ =

11.
3
lg(lgx) lg(lgx 2) 0+ − =
32.
3 1
2
log log x 0
 
≥
 ÷
 ÷
 
33.
1
3
4x 6
log 0
x
+
≥
34.
( ) ( )

− >
41.
2
2
3x
x 1
5
log x x 1 0
2
+
 
− + ≥
 ÷
 
42.
x 6 2
3
x 1
log log 0
x 2
+
−
 
>
 ÷
+
 
43.
2
2 2

x 1 x
2 2 1
2
1
log 4 4 .log 4 1 log
8
+
+ + =
15.
( )
x x
lg 6.5 25.20 x lg25+ = +
16.
( )
( ) ( )
x 1 x
2 lg2 1 lg 5 1 lg 5 5
−
− + + = +
17.
( )
x
x lg 4 5 x lg2 lg3+ − = +
18.
lgx lg5
5 50 x= −
18.
2 2
lg x lgx 3
x 1 x 1

( )
2
8
log x 4x 3 1− + ≤
25.
3 3
log x log x 3 0− − <
26.
( )
2
1 4
3
log log x 5 0
 
− >
 
27.
( )
( )
2
1 5
5
log x 6x 8 2log x 4 0
− + + − <
28.
1 x
3
5
log x log 3
2

2
6 6
log x log x
6 x 12+ ≤
48.
3
2 2
2 log 2x log x
1
x
x
− −
>
49.
( ) ( )
x x 1
2 1
2
log 2 1 .log 2 2 2
+
− − > −
50.
( ) ( )
2 3
2 2
5 11
2
log x 4x 11 log x 4x 11
0
2 5x 3x

x
logxlog
55.
( ) ( ) ( )
04221
3
3
1
3
1
<−+++−
xlogxlogxlog
56.
( )
xlogxlog
x
2
2
2
2
+
≤ 4 57.
( ) ( )
2 2
5 5
log 4 12 log 1 1x x x+ − − + <
58.
( ) ( )
12lg
2

+>+
−
−
xlogxlog
x
x
62.
( )
( )
2
3
23
33
2
3
43282 xlogxxxlogxlogxlogx
+−≥−+−
63.
220001
<+
x
log
64.
0
132
5
5
lg
<
+−