Phương trình logrit
**Phương trình cơ bản:
logaf(x) = logag(x)
0g(x)hay 0f(x)
g(x) f(x) logaf(x) = b f(x) = ab
**Các công thức logarit:
1) loga1 = 0 logaa = 1 2) b
bloga
a 3) logaab = b
4) bb a
aloglog
5) b
b
aa log)
1
(log
6) Với A>0,B>0 loga(A.B) = logaA + logaB loga(A/B) = logaA -
logaB
7) công thức đổi cơ số : logab = logcb
logca hay logab = logac.logcb
1.Giải các phương trình sau:
a) log3
x2 + 6x + 9
2x + 2 = log3(x + 1) b) lg(x2 – 6x + 7) = lg(x –3)
c) log2(x2 – x – 9) = log2(2x – 1) d) )x2(log)1x(log 2
2
1
e) xlog
2
1
4
x8
log
2
12
f)log3(2x + 1)(x – 3) = 2
g) log3(2x + 1) + log3(x – 3) = 2 h) log5(x2 – 11x + 43) = 2
i) log5–x(x2 – 2x + 65) = 2 j) log3[log2(log4x)] = 0
k) log2{3 + log6[4 + log2 (2 + log3x)]} = 2
l) log4{2log3[1 + log2(1 + 3log2x)]} = 1
2
m) 255 2logx)2logx(2 55
n) 8lgx – 3.4lgx – 6.2lgx + 8 = 0 o) log2(25x+3 – 1) = 2 + log2(5x+3 + 1)
p) log3x + log9x + log27x = 11 q) log3x
log93x = log279x
log24327x
r) )x12(log.3log21
xlog
2log21
9x
9
9
s) log2x + 2log7x = 2 + log2x.log7x
t) 1
2 log2(x – 1)2 + )4x(log
2
1 = log2(3 – x) u) )32(logx)44(log 1x
2
1
x
2
v)log2(3x – 1) + 1
log(x +3)2 = 2 + log2(x + 1)
w) log27(x2 – 5x + 6)3 =
2
1x
log
2
1
3log9(x – 3)2
.Giải các phương trình sau:
a) log3x + log9x + log27x = 11
b)log8x + log64x = 1
2
c) log3x + log9x + log81x = 7
2
d) log2x + log4x = 3log
2
1
e) log5x + log25x = 3log 2,0
f) log4(x + 3) – log4(x – 1) = 2 – log48
g) lg(x + 10) + lg(2x – 1) – lg(21x – 20) = 1 – lg5
h) log5x = log5(x + 6) – log5(x + 2)
i) log4(log2x) + log2(log4x) = 2
j) log2x + log3x + log4x = log20x
.Giải các phương trình sau:
a) (log2x)2 – 3log2x = log2x2 – 4
b) 02xlog.3xlog
3
1
3
1
c) 2xlogxlog3)x(log
2
12
2
2
d) 8
8
x
log)x4(log
2
2
2
2
1
e) log2(2x + 1).log2(2x+1 + 2) = 6
2.Giải các phương trình sau:
a)
2
1
xlog3logxlog3log 3
x
3x b) 2xlog)x2(log x2
x2
b) 2)7x3(log)3x5(log 3x57x3
c) 364log16log x2
x2 d) 04log34log24log3 x16x4x
e) 2
xxx )5(log25,2)x5(log5log f) 5lnx = 50 – xln5
g) 05x.2x.2 xlog3xlog 82 h) log5x.log3x = log5x + log3x
3.Giải các phương trình sau :
a) logx[log4(2x + 6)] = 1 b) logx[log9(2.3x + 3)] = 1
c) 8
8
x
log)x4(log
2
2
2
2
1
d) 2)22(log)64(log 2x
5
x
5
e) xlog
2
1
)
3
x
(logxlog).
x
3
(log 2
3
323
f)
2
1
)xx213(log 2
3x
g) 2log
xcos.x2sin
xsin2x2sin3
log 22 x7x7
h) 0)xcos
2
x
(sinlog)xsin
2
x
(sinlog
3
13
3.Giải các phương trình sau:
a) x26xlog)1x(xlog 2
2
2 0
b) 016)1x(log)1x(4)1x(log)2x( 3
2
3
c) xlog)x1(log 32 d) xlog)13x3x(log 2
2
3
e) 1xlog)8xx(log 3
2
4 f) )gx(cotlog2)x(coslog 32
g) )xx1(log3xlog2 3
32
4.Giải các bất phương trình sau:
a) 2)385(log 2 xx
x b) 1)
2
23
(log
x
x
x c) 1)2(log 2x
x
d) 14log.2log.2log 22 x
xx e) 1)]729([loglog 3
x
x
f) 126 6
2
6log)(log xx x g) 1)5(log)1(log)1(log 3
3
1
3
1 xxx
h)
)1(log 2
2
2
1
x
> 1 i) )3(log 2
x-3x x> 1
j)
132log
1
2
3
1 xx
> )1(log
1
3
1x k) 0
1
x
)3x(log)3x(log 3
3
1
2
2
1
l) 4
3
16
13
log).13(log
x
4
1
x
4
.Tìm miền xác định của các hàm số
a) y = 4log2x – (log2
1
x)2 – 3 + x2 – 7x + 6
b) y = lg(5x2 – 8x – 4) + (x + 3)– 0,5
c) y = lg
1 – 2x
x + 3 d) y = 17x6
3x
29x18x3
24
2