PT,BPT MŨ,LOGARIT ÔN TUYỆT VỜI

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PT, BPT MŨ VÀ LOGARIT Gv: Đoàn Văn Đông
Co dua
Doa nay
Bot net t
Ma ko thay gi
B i 1: Già ải pt
§
8
x
+ 18
x
= 2.27
x
8
x
− 7.4
x
+ 7.2
x + 1
− 8 = 0
49
x+1
+ 40.7
x+2
- 2009 = 0
9
2x +4
- 4.3
2x + 5
+ 27 = 0

5
2x + 1
- 7
x + 1
= 5
2x
+ 7
x
64 .9x – 84 .12x + 27 .
16x = 0
Bài 2: Giải BPT
x x
2.16 15.4 8 0− − =
2x 8 x 5
3 4.3 27 0
+ +
− + =
x x x 3
(3 5) 16(3 5) 2
+
+ + − =
3 4
2 2
3 9
x
x
−
−
=
3sin 1

2 9
3 4
x+
 
=
 ÷
 
cos 2 3cos
4 49
7 16
x x−
 
=
 ÷
 
2 2
3 3 30
x x+ −
+ =
1
2 2 1
x x−
− =
2 2
1 4
5 2.5 123 0
x x− −
− − =
2 2
2

2 2 3
x x x x− + −
− =
1
4 6.2 32 0
x x+
− + =
27 13.9 39.3 27 0
x x x
− + − =
cot cot
9 3 2
x x
+ =
033.369
31
22
=+−
−− xx
( ) ( )
3 2 2 2 2 1 2 1 0
x x
+ − + − − =
2
2
8 36.3
x
x
x
−

+
=
2
3 3
log log
3 162
x x
x+ =
2 5 7
x x x
+ =
3 4 5
x x x
+ =
2 2
9
log 3log
2log
2
10
x x
x
x
− −
−
=
2 2 2
3 2 6 5 2 3 7
4 4 1 4
x x x x x x− + + + + +

+ = +
( ) ( )
43232 =−++
xx
6.9 13.6 6.4 0
x x x
− + =
8.4 70.10 125.25 0
x x x
− + =
2 2
2
2 2 5
x x x x+ − −
+ =
0624 =−+
xx
0273.43
5284
=+−
++ xx
09.66.134.6 =+−
xxx
04.66.139.6
1
.6
11
=+−
+
xxx

xxx
9.21525 =+
( )
329log
2
=−+
x
x
5332
2
42
−+−
=
xxx
( )
093.823
12
=+−
+ xx
073.59 =++
xx
( ) ( )
3
2531653
+
=−++
x
xx
xxx
36.281.216.3 =+

25 2 5 15 0.
x x
− − =
4 2 1
3 -4.3 27 0
x x +
+ =
2 2
3 3 24
x x+ −
− =
1
5 2 8
2 0
2 5 5
x x+
   
− + =
 ÷  ÷
   
( ) ( )
4 15 4 15 2
x x
− + + =
3
1
( 3 2) ( 3 2)
x
x
x−

+ = −
x l x
3 2.3 7 .
+ −
+ =
2 1
3 9.3 6 0
x x+
− + =
2 2
2 9.2 2 0
x x+
− + =
1 1
4 6.2 8 0
x x+ +
− + =
x x x
6.9 13.6 6.4 0− + =
x x
(7 4 3) 3(2 3) 2 0+ − − + =
x x
2.16 15.4 8 0− − =
x x x
3.16 2.8 5.36+ =
6
2
9 3
x
x+

<
055.425 <−−
x
x
222
22121
15.34925
xxxxxx −−+−+
≥+
( ) ( )
x
xx
2.8215.7215 ≥++−
VipLam.Net
PT, BPT MŨ VÀ LOGARIT Gv: Đoàn Văn Đông
2.14
x
+ 3.49
x
– 4
x
≥ 0
3.4
x + 1
− 35.6
x
+ 2.9
x + 1
≥ 0
Bài 3: Giải Pt

( ) ( )
1
2 7
1
4 15 4 15
x
x
x
+
−
−
− ≤ +
12
3
1
3
3
1
1
12
>






+







+
xx
3 9.3 10 0
x x−
+ − <
1
1 1
( ) 8 12.( ) .
4 2
x x+
+ ≤
(
)
(
)
7 4 3 7 4 3 14
x x
− + + ≥
2 2 2
2 1 2 2 1
9 34.15 25 0
x x x x x x− + − − +
− + ≥
27 5.12 6.8 0
x x x
+ − ≥

1
9 4.3 27 0
x x+
− + ≤
1
6 4 2 2.3
x x x+
+ < +
922
7
≤+
−xx
2x 2 x x
3 2.6 - 7.4 0
+
− >
3
log log 9 3
x
x + =
1)1(loglog
22
=−+ xx
( ) ( )
8log21log3log
444
−=−−+ xx
33loglog.4
9
=+

x
x
2
2 1
2
log ( 2 8) 1 log ( 2)x x x− − = − +
2 2
log 2 log 4x 3
x
+ =
2
2 x
log x log 2 3+ =
( )
43.59log
2
=+
xx
( )
[ ]
169loglog
3
=−
x
x
( )
16log1log
12 +
=+
x

x
( ) ( )
3 3 3
log 2 log 2 log 5x x+ + − =
2
2 1
2
2
log 3log log 2x x x+ + =
( )
( )
2
2 2
log 4 log 8 2x x x− + =  + 
 
( )
2 1
1 log 1 log 4
x
x
−
+ − =
2 3
5 7lg lg lgx x x− = −
2 2
2 16 7 0 + − =. log logx x
2
2 2 2
9log log logx x x+ =
4

7
log 2 log 0
6
x
x− + =
16 2
3log 16 4log 2log
x
x x− =
2
2
log 16 log 64 3
x
x
+ =
2
2
2
log 3.log 2 0x x− + =
3 3
log log 2
4 6
x
x+ =
( )
( )
2
3 3
log 5 log 2 5x x x− − = +
( )

2 2
log 4 log 2 4x x+ = + −
( ) ( )
3 2
3.log 2 2.log 1x x+ = +
( ) ( )
2
2
2
log 4 log 2 5x x− =
( )
[ ]
{ }
2
1
log31log1log2log
3234
=++ x
VipLam.Net
PT, BPT MŨ VÀ LOGARIT Gv: Đoàn Văn Đông
log
4
(x +3) – log
4
(x
2
– 1) = 0
log
2
(9

x – 2
+7)–2 = log
2
( 3
x – 2
+ 1)
log
4
x + log
2
x + 2log
16
x = 5
log
2
x +
logx + logx = log
2x - log(5
x
+ x - 2) = log
4
x

Bài 4: Giải BPT
(
)
2
1
213log
2

3
=+−−
+
xx
x
( )
112log.loglog2
33
2
9
−+= xxx
( ) ( )
155log.15log
1
255
=−−
+xx
( )
xx
57
log2log =+
2
10 log 6 9x + =
( ) ( )
654log5.254log3
2
2
2
2
=+−−++−+ xxxx

( )
2log2log
2
2
=++
+
xx
x
x
3log3)127(log)23(log
2
2
2
2
2
+=+++++ xxxx
)112(log.log)(log2
33
2
9
−+= xxx
( ) ( )
4 2 2 4
log log log log 2x x+ =
5 25 0,2
log log log 3x x+ =
( ) ( )
2 3
4 8
2

log 1 2 log 4 log 4x x x+ + = − + +
5 25 0,2
log log log 3x x+ =
1
.log(5 4) log 1 2 log0,18
2
x x− + + = +
( )
( )
2
2 2
log 4 log 8 2x x x− + =  + 
 
4
7
log 2 log 0
6
x
x− + =
( )
2 1
1 log 1 log 4
x
x
−
+ − =
16 2
3log 16 4log 2log
x
x x− =

2
2
log 16 log 64 3
x
x
+ =
( )
15log.5log
22
5
=
x
x
( )
( )
2
2
2 2
log x x-1 log x -2 0x
 
+ − =
 
2
2 2
log x log 1 1 x+ + =
( )
( )
2
2 2
log x 4 x log 8 x 2− + = + 

 
2
2 2
2 2 0log logx x+ − =
2 1
1 1 4log ( ) log
x
x
−
+ − =
2 2
2 16 7 0. log logx x+ − =
2
2 1
2
2
log 3log log 2x x x+ + =
242
3
2log2)2(loglog
444
−=−+ xx
( )
2
2
2
2
2 log x 2 log 4 5
x +
+ + =

1)5(log)3(log
33
<−+− xx
( ) ( )
2 2
log 3 1 log 1x x+ ≥ + −
6logloglog
3
1
3
3
<++ xxx
)2(log)1(log
2
2
1
xx −≤+
( )
2 2
2 2
log 3 1 2log 0x x x+ − − + ≤
3
2
log
5 1
x
x
−
 
 ÷

 
<
( ) ( )
2 2
log 3 1 log 1x x+ ≥ + −
2
2
log 64 log 16 3
x
x
+ ≥
2 2
log log 8 4
x
x + ≤
( )
( )
114log16log
2
2
2
−≥− xx
( )
( )
04log286log
5
2
5
1
>−++− xxx

VipLam.Net
PT, BPT MŨ VÀ LOGARIT Gv: Đoàn Văn Đông
log
2
( x
2
– 4x – 5) < 4
Bài 5: Giải hpt
a)
b)
c)
d)
e)
g)
( )
165
2
2
<+− xx
x
log
( )
24311log
2
5
<+− xx
( ) ( )
xx −≤+ 2log1log
2
2

1
( )
2385log
2
>+− xx
x
1
1
12
log >






−
−
x
x
x
2
2
8 1
log 2
1
x x
x
 
+ −

≤
 ÷
 ÷
+
 
3 1
2
log log 0x
 
≥
 ÷
 ÷
 
( )
2
1 4
3
log log 5 0x
 
− >
 
1
log 2
4
x
x
 
− ≥
 ÷
 

( )
2
log 5 8 3 2
x
x x− + >
2 2
log log 8 4
x
x + ≤
2
3 3 3
log 4log 9 2log 3x x x− + ≥ −
( ) ( )
2 4
4 2
log log log log 2x x+ ≥
2 2
log 3 log 1x x+ ≥ +
( )
( )
2
2 2
log 3 2 log 14x x x− + ≥ +
( )
2
2 2
3
log 2 log 1x x− ≤
( )
2

1
log 4 2
x x
x
+
− ≤
1 1 2
2 2
1
log ( 3) log (4 ) log
6
x x+ + − >
( ) ( )
252lg15lg <−++ xx
1
2
23
log
x
>






+
+
x
x

1
1
32
log
3
≤






−
−
x
x
( )
3
4 1
5
log 4 1 log 3
2
x
x
+
+ + >






=+
=−−
25
1
1
log)(log
22
4
4
1
yx
y
xy
2 3
9 3
x 1 2 y 1
3log (9x ) log y 3

− + − =


− =





=+
=+

4loglog2
5)(log
24
22
2
yx
yx
2 2
lg x lg y 1
x y 29
+ =


+ =

4 2
2 2
log x log y 0
x 5y 4 0
− =



− + =


1
3 2 5
4 6.3 2 0
y x

x y
+

− =


− + =

