[r]
(1)bài 1:tính giá trị biểu thøc sau:
1;
log82; 2,
271
log
; 3,
log1282 2; 4,
0,25
log
; 5,
51 log 35; 6,
log
; 7,
32 log 183;
8,
3log5
; 9,
4
8
125 1log
log
81 25
;10,
3 25
5
4
1log 3log log
16
,11,
9 4
7 5
1log log
log
49 5
Bµi 2:
:tính giá trị biểu thức sau:
A,
log159 log189 log109; b,
3
6 400 45
1 1
3 3
1
2log log 3log
2
, c,
36 log log , d,
3 log log
log
Bài 3:giải pt sau:
Bµi8:pt logarit:1,
2 12logxx x 2
;2,
log29 x
x
;3
log162x3 2;4,
log23.2 1 xx
5,
3log3 log9x x
;6,
3
3 27
5
log log log
3
x x x
;7,
3
2 2
logx logx log
;8,
2 log log x x 9,
3 1 1 12 1
2
logx logx 2logx logx
;10.
64 16
log xlogx 3
;11,
2
7
log log
6
x
x
12,
log2 log4 log8 11x x x
;13,
3
2
9 9
9
5logx logx 8logx
x x x
;14;
1log log x ;
15,
2
2
log x x1 logx2x 0
;16,
log x 2 x
;17,
log76 x
x
18,
2 9
3
2 logx 5log x
;19,
1
3
logx logx
;20,
2
6
1
logxx logxx x
21,
3
4
4
logxxx logxx
;22,
3
5
3
log x log
x
;23,
1
lg lg
2
x x
;
24,
2 2 2 log log x x x x x x
;25
lg
x 9
2lg 2x1 2,26,
lg
x3
2lg
x 2
lg 0,27,
5
5
log logx
x
x
;28,
log log2x 22x log42x;29,
log4log2 log2log4x x
hd:
log2 log2 log2
4 2
1
log log log log
2
x x x
vµ
2 2
4
1 log log log log 2
2 2
log log log
x
x x
2 2
1
log log
2
2 2
log log x log x
30
x+6¿3 4− x¿3+log1
4
¿
x+2¿2−3=log1
¿
2log1
¿
;31) log2(4
x+1
+4) log2(4x+1) = log1
√2
√
1
32) logx3 + log3x = log√x3 + log3
√
x +1
2 ;33, logx(125x) log252x =
34) log3(sin x
2−sinx) + log13 (sin x
2+cos 2x) = (Đề 3);36: xlog29 = x2 3log2x – xlog23
37) log3(3x−1) log3(3x+1−3) = 6;38; c) log4log2x + log2log4x =
39) logx3 + log3x = log√x3 + log3
√
x +1 ;40:
log3x
log93x
=log279x
log8127x
41;
log x
5
log
5
x
6
log x
5
2
;42
log x
5
log x
25
log
0,23
43
2 x
log
2x
5x
4
2
;44.
2
x
3
lg(x
2x
3)
lg
0
x 1
(2)45.
1
.lg(5x
4)
lg x 1
2
lg 0,18
2
;46
log x
5
log
5
x
6
log
5
x
2
47
log x
5
log x
25
log
0,23
;48
2 x
log
2x
5x
4
2
Bài 9: giải phơng trình sau
a
log x
5
log
5
x
6
log
5
x
2
b
log x
5
log x
25
log
0,23
c
2 x
log
2x
5x
4
2
d.
2
x
3
lg(x
2x
3)
lg
0
x 1
e.
1
.lg(5x
4)
lg x 1
2
lg 0,18
2
a.
1
2
1
4
lg x
2
lg x
b.
log x
2
10 log x
2
6
0
c.
log
0,04x 1
log
0,2x
3
1
d.
3log 16
x
4 log x
16
2 log x
2d.
3log 16
x
4 log x
16
2 log x
2e.
log 16
x2
log 64
2x
3
f.
3
lg(lg x)
lg(lg x
2)
0
a.
x
3
1
log
log x
9
2x
2
b.
x x
2
log
4.3
6
log
9
6
1
c.
x
x
2
2
1
log
4
4 log
4
1
log
8
d.
x x
lg 6.5
25.20
x
lg 25
e.
x x
2 lg 1
lg 5
1
lg 5
5
f.
x
x
lg 5
x lg 2
lg3
g.
5
lg x
50
x
lg 5h.
2
3
log x log x
3
x
162
a.
2
x
lg x
x
6
4
lg x
2
;b.
log x 1
3
log 2x 1
5
2
c.
x
2 log
32
x 1
4 x log
3
x 1
16
0
;d.
2
log x 35
x
bài10 : giải phơng trình sau:
2
1
3
1) log x x 2 log 2x2 0
2¿ log
4
{
2log3[
1+log2(
1+3 log2x)
]
}
=1 3¿ log2
(
x2−1)
=log12
(x-1) 4¿ log
x
(
x2+4x −4)
=35¿ logcosx4 logcos2x2=1 6¿ log
2(x-1)
=2log2
(
x3+x+1)
7¿ log3x+log4x=log5x
8) log x
8
log x 58
1
log x
4
4
2
x
9¿3 2log1
4
(x+2)2-3=log1
(4-x)3+log1
(x+6)3
10) log2
(
x2+x+1
)
+log2(
x2− x+1)
=log2(
x4+x2+1)
+log2(
x4− x2+1)
11) 2
(
log9x)
2=log3x log3(
√
2x+1−1)
12) log2
(
x2+3x+2)
+log2(
x2+7x+12)
=3+log23log2
(
5x+2)
+2 log5x+22−3>0
1¿ xlg
2x2−3 lgx−9
2
=10−2 lgx 2¿(x-2)log3[9(x −2)]
=9(x-2)3
3¿ log2
(
3x−1)
log2(
2 3x−2)
=2 (3)5¿ log2
(
x-√
x −1)
log3(
x+√
x −1)
=log6(
x-√
x −1)
9¿ log2x+√
log2x+1=1 6¿ lg2(
x2+1)
+(
x2−5)
lg(
x2+1)
-5x2=0 10) log5(
5x
−1
)
log25(
5x+1
−5
)
=17¿ log2
[
x(x-1)2]
+log2(
x2− x)
-2=0 11) (x −1)log2[4(x−1)]=8(x −1)3
8¿
√
3+log2(
x2−4x+5)
+2√
5-log2(
x2−4x+5)
=6 14) log2x
2+log24x=3
12) log2
(
5x−1)
log2(
2 5x−2)
=2 13) 3log2x+xlog23
=6 14) log2x2+log24x=3
15) log22x −2(x −1)log2x+2x
2
−6x+5=0 16) log2
(
5x+2)
+2 log5x (4)17) 3log32x−18xlog3
1
+3>0 18) log22x −(x+1)log2x+2x −2>0
19) log3x log2x<log3x2+log2 x
4 20)
2log12
x
+x log1
2
x5
2
21) 3(log3x)
2
+xlog3x6 22)
3 4 1
5
log 4
1
log
3
2
x
x
23)
2
1
3
1) log x x 2 log 2x2 0
√
2−|
log2x|
>log2x
2
1
3
1) log x x 2 log 2x2 0
2¿ log4
{
2log3[
1+log2(
1+3 log2x)
]
}
=1 3¿ log2
(
x2−1)
=log12
(x-1)
4¿ logx
(
x2
+4x −4
)
=35¿ logcosx4 logcos2x2=1
6¿ log2(x-1)
=2log2
(
x3+x+1)
7¿ log3x+log4x=log5x