*
2
1
: -2 < x 18
Ta 4
2
1
418 x => 2 + x = 20 – t4 , 0 t < 4 20
4
4 4
4
8 4 0
t
t t t
t
<=>
-2 < x 2
2: :
2 4
1 log x 4 x 3 < 4
1 log x 3
2 2
4 3 0
3
4 3 1
4
3 0
3 1
x
x x
x x
log x 3 log x 4 x 3
> 0
<=>
2
2
log4 x2 4 x 3 > 0 <=> x < 2 - 2 V x > 2 + 2
log4 ( x – 3 ) > 0 <=> x > 4
*
Trang 2<=> x2 4 x 3 > ( x – 3 ) <=> x2– 4x + 3 > ( x – 3 )2
( 3; 2 + 2)
+ 2) ( 4; + )
log log x 1 x log log x 1 x
log log x 1 x log log x 1 x
<=>
5
5
1
2 5
5
2 5 2
2
2
2
1 5
1
1 (1 )
x
x
x
x
12
5 )
Trang 3
2
1 1
3 3
log 2 x 3 x 1 x
2
2
1
2
3 1
1 0
2
1 1
3 2
x
x x
x
x
2 2
1
2 3
1
3
1 0
3
2
1 0
1 1
x
x
x
Ta
TH 1: -1 < x < 0
TH 2: 0 < x < 1
2 V 1 < x <
3
2
TH 3: x > 3
2
2
2
2
2
log 1 log 2 3 1
<=> x2 - 3
2 ta
Trang 43 4
2
0
5 6
K
3 3 3 3 3 3 3 3 log 1 2 log 1 3 log 1 (2 log 4 3) log 4 0 0 1 6 1 6 log 4 log 1 0 : 1 0; 2 log 4 3 0 6 x x x x x x x x do x x x – 6 > 0 <=> x > 6; log3
* -1 < x < 0 => – 3
– 3
– 3
2
4 2 1 log 2 2 x x x ( 1 )
K 1 2 1 2 x x x
TH 1: 2, bpt ( 1 ) <=> 4 2
2
x
x
2 2
Trang 5TH 2: 1
2 < x
2
4 2
2
1
2
x
x
; 1 3 1; 2 2;3 7 2
2
2
2
4
x x
2
2
4
x x
2
2
Bpt ( 1 )
x
9 4
0 4 4
x x
x x
x
4 4 ; 8 16 ;
17 9 3 5
Trang 6log2 x log2 x 3 5 log 4 x 3
2x ( t 3 ),
2
2
2
3 0
3 0
3 1 0
1
t t
t
t
2
x x
2x <4 <=> 8 < x < 16
1
8;16 2
2
2 log
2
K
2
2
5 3
10 22 0
5 3
2
x
x x
x
x x
( * )
TH 1: 2 < x < 5 - 5 3 2 2 5 3
Bpt ( 1 ) <=> x2 -10x + 22< 1 <=> x2 – : 2 < x < 5 - 3
TH 2: x > 5 + 3 => log2 1
2 x Bpt ( 1 ) <=> x2 -10x + 22 > 1 <=> x2 -10x + 21 > 0 <=> x < 3 V x > 7
- 3 V x > 7
Trang 7 2 2
1 logx x x 6 4 *
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
log
x
x x
HD: 5
4 x 2
N 5
5
4< x <2 => 6 1 x < 2
6 1 x < 2 V 2 < x 5
1
Bpt ( 1 ) <=> 2 x 1 x2 2 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
Trang 85x + 2 3 4 2 2
6 x x x log x x x log x 5 5 6 x x ( 1 )
K – x 2 0 => 0 < x 3
2
2 2
2
1
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
x
x x x
<=>
5
2 < x 3
5
2 < x 3
1
2
x x x x
HD: : ( x – 2 ) ( x – 3 ) > 2
3
x x
<=> x
2– 9 > 1 10