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: Đưa về cùng cơ số
1.
x x x
2
3 2 1
2 16
2.
2
x 6x 5/2
2 16 2
3.
2
x 4x
3 1 / 243
4.
5 17
xx
9.
x
x
x
2
1
1
3
2
2 2 4
10.
2
2 5 2 1
3 27
15.
3
1 2 1 3
2 4 8 2 2 0 125. . . ,
x x x
16.
3
3
3
2 4 0 125 4 2,
xx
x
17.
4
2
4
22
4
5 .0,2 125.0,04
x
x
x
xx
x
21.
2
2 3 1
3
3 9 27 675
x
xx
22.
2 2 2 2
1 1 2
2 3 3 2
x x x x
23.
22
3 9 9
4 16 16
x
x
27.
x 4 x 3 x x 2
3 5 3 5
28.
x 1 x 2 x 4 x 3
7.3 5 3 5
29.
x x 1 x 2 x x 1 x 2
2 2 2 3 3 3
30.
3
2
9
2
2222
2
xxxx
2x 8 x 5
3 4.3 27 0
4.
1 4 2
4 2 2 6
x x x
5.
22
4 6.2 8 0
xx
6.
2
7
6.0,7 7
100
x
x
x
7.
13
3
64 2 12 0
xx
12.
22
12
9 10.3 1 0
x x x x
13.
2x 6 x 7
2 2 17 0
14.
10
5 10
3 3 84
xx
15.
2 1 1
1
.4 21 13.4
2
xx
22
2
2 2 3
21.
22
sin cos
9 9 10
xx
22.
31
53
5.2 3.2 7 0
x
x
23.
12
5 5.0,2 26
xx
24.
1
29.
1 1 1
x x x
2.4 6 9
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30.
1 1 1
6.9 13.6 6.4 0
x x x
31.
3 3 3
25 9 15 0
x x x
32.
A06
027.21812.48.3
xxxx
33.
07.714.92.2
22
39.
31
125 50 2
x x x
40.
xxx
27.2188
41.
2 3 2 3 14
xx
42.
2 3 2 3 2
xx
43.
49.
xx
(7 4 3) 3(2 3) 2 0
50.
26 15 3 2 7 4 3 2 2 3 1
x x x
51.
cos cos
5
7 4 3 7 4 3
2
xx
52.
7 3 5 7 3 5 14.2
xx
x
xx
x
57.
xx
7 4 3 7 4 3 14
58.
10625625
tantan
xx
59.
xx
x
3
5 21 7 5 21 2
60.
sin sinxx
5 2 6 5 2 6 2
64)5125.(275.95
3
xxxx
66.
2
2 6 2 6
xx
67.
xxx
9133.4
13
68.
093.613.73.5
1112
xxxx
69.
24223
2212.32.4
xxxx
2 7.2 7.2 2 0
x x x
S dng tớnh n iu ca hm s
1.
4 9 25
x x x
2.
x x x
3 4 5
3.
x
3 x 4 0
4.
x
x
4115
5.
2
2 2 2
3 2 2
xx
xx
10.
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xx
x
11.
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x
xx
12.
xxx
5.22357
13.
xx
xx 2.1.24
2
2
18.
1 1 5
3 5 3 10
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x x x
xx
x
19.
1 1 1
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3 2 6
x x x
xx
x
20.
2013 2015 2.2014
x x x
22
xxxxx
5.
22
2 ( 4 2) 4 4 4 8
x
x x x x
6.
2 1 2
4 .3 3 2 .3 2 6
x x x
x x x x
7.
20515.33.12
1
xxx
8.
2 2 2
3 2 6 5 2 3 7
4 4 4 1
13.
1224
2
22
11
xxxx
14.
22
2 1 2 2
2 9.2 2 0
x x x x
15.
2 2 2
.2 8 2 2
xx
xx
16.
2 2 2 2
.6 6 .6 6
x x x x
xx
xx
21.
22
3.16 (3 10)4 3 0
xx
xx
22. ►
2 3 1 3
4 2 2 16 0
x x x
23. ►
x x x x
4 1 3 2 1
5 25.5 26.5 5 5 0
24. ►
x x x x
1
81 4.27 10.9 4.3 3 0 Lơgarit hóa
xx
xx
x
x
3.
1
2 4 1
xx
x
4.
2
11
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2
x
xx
5.
x
xxxx
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322
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10.
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11.
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x
x
1
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22
2
12.
x
x
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2
13.
1
2
xx
x
x
17.
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xx
x 18.
3 5 6 2
xx
x
19.
xx
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20.
xx
x
2
3 2 3 2
21.
2.
2
5
log ( 2 65) 2
x
xx
3.
2
2
log 1
xx
x
4.
2
2 1/2
log ( 1) log (x 1)x
9.
4 1 3 2
21
57
xx
2
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x
x
x
15.
1
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x
x
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x x x x x x
1.
1
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xx
x
2.
x
x
7.
43
34
xx
8.
75
57
xx
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5.
55
log ( 3) log ( 2 6)xx
6.
9.
3 9 27
log log log 11x x x
10.
33
log log ( 2) 1xx
11.
93
log ( 8) log ( 26) 2 0xx
12.
2
22
log ( 3) log (6 10) 1 0xx
13.
32
1
log( 1) log( 2 1) log
2
x x x x
14.
3
4 1/16 8
log log log 5x x x
x x x
20.
3
loglog log(log 2) 0xx
21.
2
log 1 3log 1 2 log 1x x x
22.
42
log ( 3) log ( 7) 2 0xx
23.
21
8
log ( 2) 6log 3 5 2xx
24.
3
18
2
2
log 1 log (3 ) log ( 1)x x x
25.
21
2
2log log .log ( 2 1 1)x x x
31.
5 3 5 9
log log log 3.log 225xx
32.
2
3
3
log 1 log 2 1 2xx
33.
23
48
2
log ( 1) 2 log 4 log ( 4)x x x
34.
2 2 2
2 3 2 3
log ( 1 ) log ( 1 ) 0x x x x
35.
22
93
3
38.
5
log 5 4 1
x
x
39.
44
2
log 2 ( 3) log 2
3
x
xx
x
40.
23
48
2
log 1 2 log 4 log 4x x x
2log ( 2) log ( 4) 0xx
44.
log9 log
96
x
x
45.
5
5 50
log log
x
x
46.
2
log
1
log 6 5
x
x
47.
3
16
x
50.
log ( ) log ( )
xx
x
1
4 4 2 3
21
2
51.
2
2 1 2
2
1
log ( 1) log ( 4) log (3 )
2
x x x
52. D07
22
1
log (4 15.2 27) 2log 0
4.2 3
x
x
56.
3
22
log 4 1 log 2 6
xx
x
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22
22
4 2 4 2
22
log x x 1 log x x 1
log x x 1 log x x 1
60.
5
1
2log( 1) logx log
2
xx
61.
2
22
log ( 3) log (6 10) 1 0.xx
62.
2
1
log( 10) logx 2 lg4
2
x
63.
22
33
xx
x : t n ph.
1.
23
log log 2 0xx
2.
2
22
log 2log 2 0xx
3.
22
3 log log (8 ) 3 0xx
4.
2 4 2
1
2 log 1 log log 0
4
xx
5.
1
33
log (3 1).log (3 3) 6
( 1) 2
log 16 log ( 1)
x
x
11.
21
1 log ( 1) log 4
x
x
12.
2
2
log 16 log 64 3
x
x
13.
22
3
log (3 ).log 3 1
x
x
2
3
27
16log 3log 0
x
x
xx
18.
2
2
1/2 2
log 4 log 8
8
x
x
19.
23
/2 4 2
4 log 2log 3log
x x x
x x x
20.
2
3/ 3
log 2 log 1
x
25.
A08
22
2 1 1
log (2 1) log (2 1) 4
xx
x x x
26.
2
log(10 ) log log(100 )
4 6 2.3
x x x
27.
2
2 2 2
log 2 log 6 log 4
4 2.3
xx
x
28.
2/ 2
2 2 2
log 2 log 2 log log
2
x
x
x x x
34.
33
log . log 3 3 log 3 3 6
x
x
35.
4 2 2 4
log log log log 2xx
36.
8
2
3log
log
2 2 5 0
x
x
xx
37.
S dng tớnh n iu ca hm s
1.
5
log ( 3) 4xx
2.
3
log ( 3) 8xx
3.
0,5
11
log
42
xx
4.
2
22
log (x x 6) x log (x 2) 4
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13.
32
4( 2) log 2 log 3 15( 1)x x x x
x
xx
2
2 log ( 2)
6
21
:
2
4 4 1 1
x
x
có đúng 3
nghiệm thực phân biệt.4:
5.
2
33
3 log 2 4 2 log 2 16x x x x
6.
2 3 2 3
log .log 1 log logx x x x
7.
2 3 2 3
log .log log logx x x x
8.
2 2 2
4 5 20
log ( 1).log ( 1) log ( 1)x x x x x x
9.
2
22
log ( 3).log 2 0x x x x
10.
2
33
(log 3) 4 log 0x x x x
7272
log.log2log2log
16.
2
33
log ( 12)log 11 0x x x x
17.
2
22
log 2( 1)log 4 0x x x x
18.
2 3 5
2 3 2 5 3 5
log .log .log
log .log log .log log .log
x x x
x x x x x x
19.
3
3 2 3 2
31
log .log log log
2
3
x
xx
24.
2
2 7 7 2
log log 3 / 2 2 log 3 logx x x x x x
25.
1
4 2 2 2 1 sin 2 1 2 0
x x x x
y
5: Mũ hóa
1.
x x x
4
4
18
2log log
8.
2 2 3 3
log log log logxx
9.
x x x
2 3 3 2 3 3
log log log log log log
10.
2 3 4 4 3 2
log log log log log logxx
11.
2 2 2
log 9 log log 3
2
.3
x
x x x12.
3
2
3 log log
3
3
100. 10
xx
16.
2 2 2
log log 3 3log
36
xx
x
17.
9
log
2
9.
x
xx
18.
2
log
22
2
2. log
2
x
x
xx
áp 6:
PP đánh giá và dùng hàm đặc trưng.
1.
Tran Quang Time goes, you say? Ah, no! Alas, time stays, we go 5.
2
2
2
2
1
log 3 2
2 4 3
xx
xx
xx
6.
11
1
37
log 30 3 3.7
4.7 30
xx
xx
x
9.
2
1
12
22
2 .log ( 1) 4 .(log 1 1)
x
x
xx
10.
sin( )
4
tan
x
ex
11.
2 1 3 2
x
x
x
14.
log 1 lg 4,5 0
x
x
A02: Cho phng trỡnh
22
33
log log 1 2 1 0x x m
(1) (m l
tham s)
a) Gii phng trỡnh (1) khi m = 2.
b) Tỡm m phng trỡnh (1) cú ớt nht
mt nghim thuc on
3
1 ; 3
.
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4.
2
2 16
11
( ) ( )
39
x x x
5.
1
2
1
1
2
16
x
x
2
2
56
11
3
3
x
xx
11.
2
27
21
xx
x
12.
11
2 2 3 3
x x x x
13.
1
16.
2 6 7
2 2 17 0
xx
17.
3
2 2 9
xx
18.
2.49 7.4 9.14
x x x
19.
5.2 7. 10 2.5
x x x
20.
1
4 3.2 4
x x x x
21.
2 2 2
7
xx
25.
12
3
1
3
3
1
1
12
xx
13.43
224
2
xx
x
30.
8log.2164
4
1
xx
31.
52824
3
12
12
x
xx
32.
02
2
35.
11
2
x
xx
36.
2 2 2
2 2 2
6.9 13.6 6.4 0
x x x x x x
37.
xx
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222
38.
62.3.23.34
212
xxxx
xxx
x
x
x
42.
12log
log
1
1
3
35
12,0
x
x
x
x
xx
x
46.
125.3.2
2log1loglog
222
xxx
47.
23.79
1212
22
xxxxx
48.
32
4log
2
x
x
49.
1282.2.32.4
222
2.
123log
2
2
1
xx
3.
243log1243log
2
3
2
9
xxxx
4.
3
1
6
5
log
3
x
x
x
x
x
x
2
2
1
2
2
3
2
2
1
4
2
log.4
32
log9
8
loglog
48loglog
22
x
x
11.
01628
1
5
log134
2
5
2
xx
x
x
xx
12. 03log7164
3
2
xxx
log.log1loglog
16.
1log
1
132log
1
3
1
2
3
1
x
xx
17.
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2
2
xx
18.
24311log
2
x
x
xx
22.
1
8
218
log.218log
24
x
x
23. 193loglog
9
27.
x
xx
x
xx
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2
log2242141
2
1272
22
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2
xx
31.
015log
3,0
xx
32.
0
352
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2
3
2
11
2
2
5
xx
xxx
33.
2
3
2
9
x
x
35. 3
2
1
2
1
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2
1
xx
36.
1log
2
1
log
2
3
2
3
4
xx
37.
40.
0
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2
2
1
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1
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1
log41log.91
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2
x
x
x
46.
1
1
12
log
x
x
x
47.
1
log1
log1
3
2
3
1
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2
1
2
xx
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51.
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2
1
log
7
7
xx
52.
0
43
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2
3
3
2
2
x
x
56.
0loglog
2
4
1
2
2
1
xx
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57.
2log2log
12
xxx
58.
1log.
112
1
x
x
x
2
2
1
2
2
3
2
2
1
4
2
log4
32
log9
8
loglog
63.
33
log x log x 3 0
64.
2
14
3
log log x 5 0
65.
2
15
5
log x 6x 8 2 log x 4 0
66.
1x
3
5
log x log 3
71.
5x
log 3x 4.log 5 1
72.
2
3
2
x 4x 3
log 0
x x 5
73.
13
2
log x log x 1
74.
2
2x
log x 5x 6 1
2
22
log x log x 0
78.
xx
2
16
1
log 2.log 2
log x 6
79.
2
3 3 3
log x 4 log x 9 2 log x 3
80.
24
1 2 16
2
log x 4log x 2 4 log x
81.
13
3
5
4
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x
y
xy
2.
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x
y
y
x
33
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324
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xy
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y
x
11)
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453log53log
xyyx
xyyx
yx
yx
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33
xy
yx
xy
14)
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8loglog.5
4
3
2
2
42
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15)
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17)
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3log12loglog
4
2
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22
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y
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18)
y
x
x
y
33
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324
20)
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yx
x
813.122
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2
3
21)
2
xyxxyx
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y
x
x
23)
22
lg x lg y 1
x y 29
24)
3 3 3
log x log y 1 log 2
x y 5
25)
xy
yx
33
4 32
log x y 1 log x y
28)
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2
xy
2 log x
log xy log x
y 4y 3
29)
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22
31)
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93
1 2 1
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xy
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32)
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3
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35)
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4096
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x
36)
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log log 0
xy
xy
39)
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22
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xy
xy
x y x y
40)
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ln(1 ) ln(1 )
12 20 0
x y x y
x xy y
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