MU-LOGA CAP TOC 2009

1) (A07)
3 1
3
2log (4 3) log (2 3) 2 + + x x
(
3
3
4
x<
)
2) (D305)
2
2 4 2
3
log log ( 4 4) log 3
2
x
x x
x
+
+ + + >

(x>2
4x <
)
3) (D206)
2 4 2
1
2(log 1) log log 0
4
x x+ + =

( x=2

x= ẳ)
4) (B203)
0,5 0,25 2
log 2log ( 1) log 6 0x x
+ +
(x 3)
5)
8
4 2
2
1 1
log ( 3) log ( 1) log (4 )
2 4
x x x+ + =
(x = 3

x= 3+
12
)
6) (B104)
1
2 4 16
4
2
x
x
x

+
>

(x<2

x> 4)
7) (A104)
2
2
4
log [log ( 2 )] 0x x x

+ <
(x >1 x< - 4)
8) (B204)
3
log log 3
x
x >
( x>3

1/3 <x <1)
9) (D03)
2 2
2
2 2 3
x x x x +
=
(x =1

x=2)
10) (D2.05)
3
3
1
.29
2
2
2
2










xx
xx
.. (
1 2 1 2x +
)
11) (B206)
2 2
1 2
9 10.3 1 0
x x x x+ +

+ =
( x=1

x=2)
12) (A.06) 3.8
x
+4.12
x
18
x
2.27
x
=0 (x=1)
13) (D06)
2 2
2
2 4.2 2 4 0
x x x x x+
+ =
( x=0

x=1)
14) (CHQ 05)
1 2 1
2
3 2 12 0
x
x x+ +
<
(x >0)

15) (B07)
( ) ( )
2 1 2 1 2 2 0
x x
+ =
(x = 1)
16) (D203)
5
log (5 4) 1
x
x =
(x =1)
17) (B06)
2
5 5 5
log (4 144) 4log 2 1 log (2 1)
x x

+ < + +
(2<x<4)
18) (B02)
3
log (log (9 72)) 1
x
x

(
9
log 73 2x<
)

19) (D07)
( )
2 2
1
log 4 15.2 27 2log 0
4.2 3
x x
x
+ + + =

2
( log 3)x =
20) (D106)4
x
2
x+1
+2(2
x
1)sin(2
x
+y 1) +2 =0 (x =1, y =
2
p
1 +k2)
21) (D106)
1
3 3
log (3 1) log (3 3) 6
x x+
=

( x=
3
log 10

x=
3
28
log
27
)
22) (D102) 16
3
2
3
27
log 3log 0
x
x
x x =
(x=1)
23) (A102)
2 1
1 0,5
2
log (4 4) log (2 3.2 )
x x x+
+
( x 2)
24) (A204)2
2 2

1 3
log log
2 2
2
x x
x

(0 < x 2

x4)
25) (A203)
1 1
15.2 1 2 1 2
x x x+ +
+ +
(x 2)
26) (D103) f(x)=
log 2.
x
x
. Gii bpt f (x)0 (0 < x e

x 1)
27) (B3-03)
3 2 3 2
x x
x+ = +
( x=0

x=1)

28)
2 2 2
log 9 log log 3
2
3
x
x x x=
(x = 2 )
29)
5 5
log 3 log
4
x
x x+ =
(x=25)
30)
2 2
2 3
log ( 5 5 1) log ( 5 7) 2x x x x
+ + + +
(
5 5 5 5
1 4
2 2
x x
+

)
31) (A-08)
2 2

2x-1 x 1
log (2x x 1) log (2x-1) 4
+
+ - + =
5
x 2;x
4
= =
32) (B-08)
2
0,7 6
log log 0
4
ổ ử
+
ữ
ỗ
<
ữ
ỗ
ữ
ố ứ
+
x x
x
( 4; 3) (8; )- - ẩ +Ơ
33) (D-08)
2
1
2

3 2
log 0
- +

x x
x
) (
2 2;1 2;2 2
ộ ự
- ẩ +
ở ỷ
34) (A1-08)
1
2
3
2 3
log (log ) 0
1
+

+
x
x
x < 1
35) (A1-08)
sin( )
4
tan
p
-

=
x
e x
x= /4 + k
36) (A2-08)
3
1 6
3 log (9 )
log
+ = -
x
x
x x
x =
2
37) (B1-08)
1
2
2
2log (2 2) log (9 1) 1+ + - =x x
x= 1; x =
3
2
38) (B2-08)
2 1 2 1
3 2 5.6 0
+ +
- - Ê
x x x
2

3
1
log
2
Êx
39) (D1-08)
2 2
2 4 2 2 1
2 16.2 2 0
- - - -
- - Ê
x x x x
1 3 1 3- Ê Ê +x
40) (D1-07)
2 2
1
2
2
1 1
log 2 3 1 log ( 1)
2 2
- + + - x x x
1 1
3 2
Ê <x
41) (D2-07)
2
2 1
log 1 2
-

= + -
x
x
x
x
x= 1
42) (D2-07)
3 1 2
2 7.2 7.2 2 0
+
- + - =
x x x
x= 0; 1
43) (A1-07)
2
4 2
(log 8 log )log 2 0+
x
x x
1
0 1
2
< Ê >x x
44) (A2-07)
4 2
2 1
1 1
log ( 1) log 2
log 4 2
+

- + = + +
x
x x
x =
5
2
45) (B1-07)
2
3
3
log ( 1) log (2 1) 2- + - =x x
x=2
46) (B2-07)
3 9
3
4
(2 log )log 3 1
1 log
+ - =
-
x
x
x
x=
1
3
; x= 81