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chuyen de III bat phuong trinh mu va logarit.

Chuyªn ®Ị IIICác Phương Pháp Giải
Bất Phương Trình Mũ và Logarit.
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> ⇔ > >log log
a a
x y x y nếu a
 
> ⇔ < < <
log log
a a
x y x y nếu a
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Bài 1:
1)
( )
( )
114log16log
2
2
2
−≥−
xx
2)
( ) ( )
2l g 1 . 5 l g 5 1o x o x
 
− > − +
 
3)
12log
3
<−
x
4)
1
1
32
log
3
<


x
x
6)
03loglog
3
3
2
≥−
x
7)
( )
[ ]
113loglog
2
2
1
−>+
x
8)
( )
2385log
2
>+− xx
x
9)
0
1
13
log
2
>
+

x
x
x
10)
( )
( )
12log
log
5,0
5,0
2
25
08,0










x
x
x
x

11)
( )
322
2
2
2
loglog
≤+
xx
x
12)
( )
3
3
1
3
1
11loglog
2
1
−+<
xx
14)
2
4
1
log








x
x
15)
( )
12log
log
1
1
3
35
12,0










x
x
x
x

1 0
1 0
> ⇔ − − >
> ⇔ − − >
1 21 2
& & 1 21 2
x y
a a
a a a x y
x y a x y


 

log
log log
log
:
log log
>
> ⇔ >
> ⇔ >
> ⇔ > >
> ⇔ >
< <
> ⇔ <
> ⇔ < <
x y
x
a
a a
b
a
x y
a a
Nếu a thì
a a x y
a b x b
x y x y
x b x a
Nếu a thì
a a x y
x y x y
16)
22004log1
<+
x
17)
( )
( )
3
5log
35log
3
>


x
x
a
a
18)
( )
0)12(log322.124
2
≤−+−
x
xx
19)
2
1
2
24
log
2











x
x
x
20)
( )
1log
1
132log
1
3
1
2
3
1
+
>
+−
x
xx
21)
x
x
x
x
2
2
1
2
2
3
2
2
1
4
2
log4
32
log9
8
loglog
<






+









22)
( )
( )
04log286log
5
2
5
1
>−++−
xxx
23)
( )
[ ]
05loglog
2
4
2
1
>−
x
24)
( )
165
2
2
<+−
xx
x
log
25)
15
2
log
3
<

x
x
26)
( )
1
1
13log
3



x
x
27)
( )
( )
3
2
1
2
1
21log1log
2
1
−+>−
xx
28)
( )
22log1log
2
2
2
−−<+
xx
Bài 2:
1)
( )
032log225log
25
2
>−++
+
x
x
2)
03183
2
1
log
log
3
2
3
>+−
x
x
3)
( )
022log1log
2
2
2
>−++−
xxxx
4)
4
logloglog.log
2
2
323
x
xxx
+<
5)
2
5
2
2
2
1
2
2
1
loglog
>+
xx
x
6)
( )
63
3
2
3
loglog
≤+
xx
x
7)
( )
3
4 1
5
log 4 1 log 3
2
x
x
+
+ + >
8)
xx
22
loglog2
>−
Bài 3: gii cc bt phương trnh sau:
a)
2
16 4 111 2 1 2x x− ≤ −
b)
2 0 5
15
2 2
16
0
& 3& 4
x
 
− ≤
 ÷
 
c)
2 2
2 1 5 1& 1 2 & 1 2x x− > − +
d)
4
3
4
2
& &
x
x − ≤
52
1 3 1 3
4
3
2 3
& & 1 2
x
x
x
+
< −

62
2
3 1
0
1
&
x
x
x

>
+
2
2
0 5
4 6
0
7
&
x x
x
− +
<
2
1 2 2
1 2
0
1
& &
x
x
+
 
>
 
+
 
(2
1 3
3 1
2 1
&
x
x

+ <
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2 3
x x
>
'2
2
2 7
3 11 2
x x
x

− >
%2
1
4 2 3
x x+
< +
92
2 3 7 3 1
6 2 30
x x x+ + −
<
52
2 1
0 5
0 5
5 2
0 08
2
& 1 2
1 7 2
1 7 2
&
1 7 2
x
x
x
x



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