ĐỀ THI THỬ ĐẠI HỌC NĂM HỌC 2012-2013 MÔN TOÁN ĐỀ 28 docx
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*
4
21
2
1
log 2 log 4 18 0
2
xx
: -2 < x
18
Ta
4
21
2
1
log 2 log 4 18 0
2
xx
<=>
24x
4
18 x
( 1 )
4
18 x
=> 2 + x = 20 t
4
, 0
t <
4
20
4
4
4
2
42
4
4
4
4 4 4
32
0 20
0 20
0 20
8 4 0
20 4
20 4
0 20
2 20 2 18 20
2 2 5 2 0
16 18 20 2 2
t
t
t
t t t
tt
tt
t
tx
t t t t
xx
<=>
-2 < x
2
2: :
2
4
1
log 4 3xx
<
4
1
log 3x
2
2
4 3 0
3
4 3 1
4
30
22
31
xx
x
xx
x
x
x
x
2
4
4
11
log 3
log 4 3
x
xx
> 0
<=>
2
44
2
44
log 4 3 log 3
log 4 3.log 3
x x x
x x x
> 0 ( 1 )
log
4
2
43xx
> 0 <=> x < 2 -
2
V x > 2 +
2
log
4
( x 3 ) > 0 <=> x > 4
*
TH 1: x > 4, bpt ( 1 ) <=> log
4
2
43xx
> log
4
( x 3 )
<=>
2
43xx
> x 3 <=> x
2
4x + 3 > ( x 3 )
2
x > 4
TH 2: 2 +
2
< x < 4, log
4
2
43xx
> 0log
4
( x 3 ) < 0 => bpt
TH 3: 3 < x < 2 +
2
, bpt ( 1 ) <=> log
4
2
43xx
> log
4
( x 3 )
<=>
2
43xx
> ( x 3 ) <=> x
2
4x + 3 > ( x 3 )
2
( 3; 2 +
2
)
+
2
) ( 4; +
)
22
1 5 3 1
35
log log 1 log log 1x x x x
22
1 5 3 1
35
log log 1 log log 1x x x x
<=>
22
3 1 3 5
5
22
3 1 5
5
1
2 2 2 2
55
2
5
22
5
2
5
2
2
log log 1 log log 1 0
log log 1 .log 1 0
log 1 .log 1 1 : 1 1
log 1 1
log 1 1
log 1 0
15
11
x x x x
x x x x
x x x x do x x x x
xx
xx
xx
xx
xx
2
22
2
22
50
12
15
1 (5 )
5
10
1
1 1 0
10
01
1 (1 )
x
x x x
xx
x
x
x x x
x
x
xx
12
5
)
2
1
1
3
3
11
log 1
log 2 3 1
x
xx
( 1 )
2
2
10
1
2 3 1 0
0
2
2 3 1 1
3
1
10
2
11
3
2
x
xx
x
xx
x
x
x
x
2
2
1
2
3
1
3
1
0
2 3 1 0
2
log 2 3 1 0
3
2 3 1 1
1
2
10
log 1 0 1 0
11
x
xx
xx
xx
x
x
xx
x
Ta
TH 1: -1 < x < 0
TH 2: 0 < x <
1
2
V 1 < x <
3
2
TH 3: x >
3
2
2
11
2
33
11
2
33
11
33
2
log 1 log 2 3 1
0 log 1 log 2 3 1 0
log 1 .log 2 3 1
1 2 3 1
x x x
x x x
x x x
x x x
<=> x
2
-
3
2
ta
13
) (1; ) 5;
22
23
34
2
log 1 log 1
0
56
xx
xx
2
1 0 1
5 6 0 6
xx
x x x
3
3
33
3
3
3
3
log 1
2log 1 3.
log 1 (2log 4 3)
log 4
00
1 6 1 6 .log 4
log 1
0 : 1 0;2log 4 3 0
6
x
x
x
x x x x
x
do x
x
x 6 > 0 <=> x > 6; log
3
* -1 < x < 0 =>
3
3
3
2
4 2 1
log
22
x
x
x
( 1 )
1
2
1
2
x
x
x
TH 1:
2, bpt ( 1 ) <=>
42
4 2 2
2
x
x x x x
x
2
2
4 2 ( 2) 6 2 0
22
2 3 7
4 2 (2 )
12
2 2 0
12
12
x x x x x
xx
x
x x x
x
xx
x
x
TH 2:
1
2
< x
2
42
4 2 2 4 2 (2 )
2
1
2 2 0 1 3
2
x
x x x x x x x
x
x x x
1
; 1 3 1;2 2;3 7
2
S
2
2
2
log 4 5
4
x
x
2
2
2
log 4 5
4
x
x
2
11
22
2
11
22
22
2
log 4 0 3 log 2
4 8(1)
44
4
2 2 1 2 1
log 9 2 log 3 (2)
4 4 8 4 4
xx
x
xx
x
x x x
x x x
Bpt ( 1 )
2 32 10
8 0 0
8 16
44
2 6 16
35
4 0 0
44
xx
xx
x
xx
xx
Bpt ( 2 )
94
21
0
0
4. 4
44
44
2 1 17 4
17 9
00
4 8 8 4
x
x
x
x
x
xx
xx
4 4 8 16
;;
17 9 3 5
2 2 2
2 2 4
log log 3 5. log 3x x x
2
x ( t
3 ),
2
2
2
2
2
2 3 5 3
30
30
3 . 1 0
2 3 0
10
30
30
1 5 3
2 3 5 3
3 . 1 5 3
1
34
t t t
t
t
tt
tt
t
t
t
tt
t t t
t t t
t
t
V
1,t
2
1
log 1 0
2
xx
2
x <4 <=> 8 < x < 16
1
8;16
2
2
2
log
2
log 10 22 0
x
xx
( 1 )
2
2
53
10 22 0
2 5 3
53
0 log 1
53
2
12
2
x
xx
x
x
x
x
x
( * )
TH 1: 2 < x < 5 -
22
5 3 5 3
3 1 0 log log 1
2 2 2 2
xx
Bpt ( 1 ) <=> x
2
-10x + 22< 1 <=> x
2
: 2 < x < 5 -
3
TH 2: x > 5 +
3
=>
2
log 1
2
x
Bpt ( 1 ) <=> x
2
-10x + 22 > 1 <=> x
2
-10x + 21 > 0 <=> x < 3 V x > 7
-
3
V x > 7
2
2
1
log 6 4 *
x
xx
2
0 1 1 1
6 0 0, 2
xx
x x x x
x
2
+ x 6 > 0 <=> x < -3 V x > 2
TH 1: - 1 < x < 0 => x
2
+ x )<=>- (x
2
+ x 6)
( x +1)
2
<=> 2x
2
+ 3x 5
0 <=> x
-
5
2
V x
1 (VN )
TH 2: 0 < x <2 => x
2
- (x
2
+ x 6)
( x +1)
2
<=> 2x
2
+ 3x 5
0 <=> -
5
2
x
1 => 0 < x
1
TH 3: x > 2, bpt (*)<=> x
2
+ x 6
( x +1)
2
<=> x
- 7 ( VN )
1
2
4 5 1
log
22
x
x
x
HD:
5
4
x
2
N
5
5
4
< x <2 =>
61
x < 2
61
x < 2 V 2 < x
5
2
2
22
1
log 2 1 log 2 0
2
x x x
( 1 )
2
2 1 0 0
2 0 2
xx
x x x
Bpt ( 1 ) <=>
2
2 1 2x x x
( 2 )
TH 1: x < 0, bpt ( 2 ) <=> - ( 2x 1 )
x
2
2x <=> -1
x < 0
TH 2: x > 2, bpt ( 2 ) <=> 2x 1
x
2
2x <=> x
2
4x + 1
0 <=> 2 < x
2 +
3
-1
x < 0 V 2 < x
2 +
3
5x +
2 3 4 2 2
22
6 .log log 5 5 6x x x x x x x x x
( 1 )
x
2
0 => 0 < x
3
2
2 2 2
2
2
6 log 5 log 5 log 5 0
log 5 ( 6 1) 0 2
x x x x x x x x x
x x x x x
22
2
2
2
6 1 0 6 1
01
01
01
13
13
5
1
2 3 5 0
2
61
x x x x x x
x
x
x
x
x
x
xx
x x x
2
x
0 => x log
2
x
0 => x log
2
x 5 < 0 => bpt ( 2 )
3 => 0 < log
2
x
log
2
3
1 < x
3
=> x.log
2
x
3. log
2
3 => x.log
2
x - 5
log
2
2
13
6 1 0
x
x x x
<=>
5
2
< x
3
5
2
< x
3
2
3 1 1
33
1
log 5 6 log 2 log 3
2
x x x x
HD:: ( x 2 ) ( x 3 ) >
2
3
x
x
<=> x
2
9 > 1
10
