[r]
(1)bài 1:tính giá trị biểu thøc sau:
1;log82 ; 2, 27
1
log
; 3, log1282 2 ; 4, 0,2
5
log
; 5,51 log 35
; 6, log
; 7,32 log 183
; 8, 3log
5 ; 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 12
logxx x 2;2, log29
x
x
;3 log162x3 2;4, log23.2 1 x
x
5,3log3 log9
x 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 1
2 1
2
logx logx 2logx logx
;10.
64 16
log xlogx 3 ;11,
2
7
log log
6
x
x
12,log2 log4 log8 11
x 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
;25lgx 92lg 2x1 2 ,26, lgx3 2lgx 2lg 0,
27,
5
5
log logx
x
x ;28,log log2x 22x log42x;29,log4log2 log2log4
x 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 x5 log5x6 log x5 2 ;42 log x5 log x25 log0,2 3
43
2 x
log 2x 5x4 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 x5 log5x6 log5x2
47 log x5 log x25 log0,2 3 ;48
2 x
log 2x 5x4 2
Bài 9: giải phơng trình sau a log x5 log5x6 log5x2
b log x5 log x25 log0,2 3 c
2 x
log 2x 5x4 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 2lg x
b.log x2 10 log x2 6 0 c. log0,04x 1 log0,2x 3 1 d.3log 16x 4 log x16 2 log x2
d.3log 16x 4 log x16 2 log x2 e.log 16x2 log 642x 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
xlg 5 x lg 2lg3
g.5lg x 50 xlg 5h.
2
3
log x log x
3 x 162
a.
2
xlg x x 6 4 lg x2
;b.log x 13 log 2x 15 2
c.x2 log 32x 1 4 x log 3x 1 160;d.2log 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)=log1
2
(x-1) 4¿ log
x(x2+4x −4)=3
5¿ logcosx4 logcos2x2=1 6¿ log
2(x-1)
=2log2(x3+x+1)
7¿ log3x+log4x=log5x 8) log x 8 log x 58 1log 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+log23
log2(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(5
x
−1) log25(5
x+1
−5)=1
7¿ 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) log2
x
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)=log1
2
(x-1)
4¿ logx(x
2
+4x −4)=3
5¿ logcosx4 logcos2x2=1
6¿ log2(x-1)
=2log2(x3+x+1)
7¿ log3x+log4x=log5x
1
8) log x 8 log x 58 log x 4 4
2 x
(5)