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LOGARITHM HELP PLEASE!!ASAP!!!!!!!!











































Solve for x

a) 9^(1/2x^2-1)+1=4

b) 5^(2x-1)=2^(1-x)

c) log_base 2_(x+4)+log(x-2)=4

d) log(7x-12)=2logx

Comments for LOGARITHM HELP PLEASE!!ASAP!!!!!!!!

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Apr 23, 2011
Equations Involving Logarithms
by: Staff



-------------------------------------------------

Part II c

5.35, -0.24999
5.36, -0.24715
5.37, -0.24432
5.38, -0.2415
5.39, -0.23868
5.4, -0.23586
5.41, -0.23305
5.42, -0.23025
5.43, -0.22745
5.44, -0.22465
5.45, -0.22187
5.46, -0.21908
5.47, -0.21631
5.48, -0.21353
5.49, -0.21077
5.5, -0.208
5.51, -0.20525
5.52, -0.2025
5.53, -0.19975
5.54, -0.19701
5.55, -0.19427
5.56, -0.19154
5.57, -0.18881
5.58, -0.18609
5.59, -0.18337
5.6, -0.18066
5.61, -0.17796
5.62, -0.17525
5.63, -0.17256
5.64, -0.16987
5.65, -0.16718
5.66, -0.1645
5.67, -0.16182
5.68, -0.15915
5.69, -0.15648
5.7, -0.15381
5.71, -0.15115
5.72, -0.1485
5.73, -0.14585
5.74, -0.14321
5.75, -0.14057
5.76, -0.13793
5.77, -0.1353
5.78, -0.13267
5.79, -0.13005
5.8, -0.12743
5.81, -0.12482
5.82, -0.12221
5.83, -0.11961
5.84, -0.11701
5.85, -0.11442
5.86, -0.11183
5.87, -0.10924
5.88, -0.10666
5.89, -0.10408
5.9, -0.10151
5.91, -0.09894
5.92, -0.09637
5.93, -0.09381
5.94, -0.09126
5.95, -0.08871
5.96, -0.08616
5.97, -0.08362
5.98, -0.08108
5.99, -0.07854
6, -0.07601
6.01, -0.07349
6.02, -0.07096
6.03, -0.06845
6.04, -0.06593
6.05, -0.06342
6.06, -0.06092
6.07, -0.05841
6.08, -0.05592
6.09, -0.05342
6.1, -0.05093
6.11, -0.04845
6.12, -0.04597
6.13, -0.04349
6.14, -0.04101
6.15, -0.03854
6.16, -0.03608
6.17, -0.03362
6.18, -0.03116
6.19, -0.0287
6.2, -0.02625
6.21, -0.02381
6.22, -0.02136
6.23, -0.01893
6.24, -0.01649
6.25, -0.01406
6.26, -0.01163
6.27, -0.00921
6.28, -0.00679
6.29, -0.00437
6.3, -0.00196
6.31, 0.00045
6.32, 0.002855
6.33, 0.005256
6.34, 0.007654
6.35, 0.010048
6.36, 0.012439
6.37, 0.014825
6.38, 0.017209
6.39, 0.019588
6.4, 0.021964
6.41, 0.024337
6.42, 0.026706
6.43, 0.029071
6.44, 0.031433
6.45, 0.033791
6.46, 0.036146
6.47, 0.038497
6.48, 0.040845
6.49, 0.043189
6.5, 0.04553
6.51, 0.047867
6.52, 0.050201
6.53, 0.052532
6.54, 0.054859
6.55, 0.057182
6.56, 0.059503
6.57, 0.06182
6.58, 0.064133
6.59, 0.066443
6.6, 0.06875
6.61, 0.071054
6.62, 0.073354
6.63, 0.075651
6.64, 0.077944
6.65, 0.080234
6.66, 0.082521
6.67, 0.084805
6.68, 0.087086
6.69, 0.089363
6.7, 0.091637
6.71, 0.093907
6.72, 0.096175
6.73, 0.098439
6.74, 0.1007
6.75, 0.102958
6.76, 0.105213
6.77, 0.107465
6.78, 0.109713
6.79, 0.111958
6.8, 0.114201
6.81, 0.11644
6.82, 0.118676
6.83, 0.120908
6.84, 0.123138
6.85, 0.125365
6.86, 0.127588
6.87, 0.129809
6.88, 0.132026
6.89, 0.134241
6.9, 0.136452
6.91, 0.138661
6.92, 0.140866
6.93, 0.143068
6.94, 0.145268
6.95, 0.147464
6.96, 0.149658
6.97, 0.151848
6.98, 0.154035
6.99, 0.15622
7, 0.158402
7.01, 0.16058
7.02, 0.162756
7.03, 0.164929
7.04, 0.167099
7.05, 0.169266
7.06, 0.17143
7.07, 0.173591
7.08, 0.17575
7.09, 0.177905
7.1, 0.180058
7.11, 0.182208


Apr 23, 2011
Equations Involving Logarithms
by: Staff


-------------------------------------------------

Part II b

3.75, -0.80277
3.76, -0.79843
3.77, -0.79411
3.78, -0.78981
3.79, -0.78552
3.8, -0.78125
3.81, -0.777
3.82, -0.77276
3.83, -0.76854
3.84, -0.76433
3.85, -0.76014
3.86, -0.75596
3.87, -0.75179
3.88, -0.74765
3.89, -0.74351
3.9, -0.73939
3.91, -0.73529
3.92, -0.7312
3.93, -0.72712
3.94, -0.72306
3.95, -0.71901
3.96, -0.71498
3.97, -0.71095
3.98, -0.70695
3.99, -0.70295
4, -0.69897
4.01, -0.695
4.02, -0.69105
4.03, -0.6871
4.04, -0.68317
4.05, -0.67926
4.06, -0.67535
4.07, -0.67146
4.08, -0.66758
4.09, -0.66371
4.1, -0.65986
4.11, -0.65602
4.12, -0.65218
4.13, -0.64837
4.14, -0.64456
4.15, -0.64076
4.16, -0.63698
4.17, -0.6332
4.18, -0.62944
4.19, -0.62569
4.2, -0.62195
4.21, -0.61823
4.22, -0.61451
4.23, -0.6108
4.24, -0.60711
4.25, -0.60342
4.26, -0.59975
4.27, -0.59609
4.28, -0.59243
4.29, -0.58879
4.3, -0.58516
4.31, -0.58154
4.32, -0.57793
4.33, -0.57433
4.34, -0.57074
4.35, -0.56716
4.36, -0.56359
4.37, -0.56002
4.38, -0.55647
4.39, -0.55293
4.4, -0.5494
4.41, -0.54588
4.42, -0.54236
4.43, -0.53886
4.44, -0.53537
4.45, -0.53188
4.46, -0.52841
4.47, -0.52494
4.48, -0.52148
4.49, -0.51804
4.5, -0.5146
4.51, -0.51117
4.52, -0.50775
4.53, -0.50433
4.54, -0.50093
4.55, -0.49754
4.56, -0.49415
4.57, -0.49077
4.58, -0.4874
4.59, -0.48404
4.6, -0.48069
4.61, -0.47735
4.62, -0.47401
4.63, -0.47068
4.64, -0.46736
4.65, -0.46405
4.66, -0.46075
4.67, -0.45746
4.68, -0.45417
4.69, -0.45089
4.7, -0.44762
4.71, -0.44436
4.72, -0.4411
4.73, -0.43786
4.74, -0.43462
4.75, -0.43138
4.76, -0.42816
4.77, -0.42494
4.78, -0.42173
4.79, -0.41853
4.8, -0.41534
4.81, -0.41215
4.82, -0.40897
4.83, -0.4058
4.84, -0.40264
4.85, -0.39948
4.86, -0.39633
4.87, -0.39318
4.88, -0.39005
4.89, -0.38692
4.9, -0.3838
4.91, -0.38068
4.92, -0.37757
4.93, -0.37447
4.94, -0.37138
4.95, -0.36829
4.96, -0.36521
4.97, -0.36214
4.98, -0.35907
4.99, -0.35601
5, -0.35295
5.01, -0.34991
5.02, -0.34687
5.03, -0.34383
5.04, -0.3408
5.05, -0.33778
5.06, -0.33477
5.07, -0.33176
5.08, -0.32876
5.09, -0.32576
5.1, -0.32277
5.11, -0.31979
5.12, -0.31681
5.13, -0.31384
5.14, -0.31088
5.15, -0.30792
5.16, -0.30497
5.17, -0.30202
5.18, -0.29908
5.19, -0.29614
5.2, -0.29322
5.21, -0.29029
5.22, -0.28738
5.23, -0.28447
5.24, -0.28156
5.25, -0.27866
5.26, -0.27577
5.27, -0.27288
5.28, -0.27
5.29, -0.26713
5.3, -0.26426
5.31, -0.26139
5.32, -0.25853
5.33, -0.25568
5.34, -0.25283


-------------------------------------------------


Apr 23, 2011
Equations Involving Logarithms
by: Staff


-------------------------------------------------

Part II a

Footnote: Part c)

Data points used to plot graph
(data points were generated using Microsoft Excel)


log_base 2_(x+4)+log(x-2)=4

x, f(x)

2.1, -2.39119
2.11, -2.34743
2.12, -2.30729
2.13, -2.27017
2.14, -2.23563
2.15, -2.20332
2.16, -2.17295
2.17, -2.14428
2.18, -2.11712
2.19, -2.09131
2.2, -2.0667
2.21, -2.04319
2.22, -2.02066
2.23, -1.99904
2.24, -1.97824
2.25, -1.9582
2.26, -1.93886
2.27, -1.92017
2.28, -1.90208
2.29, -1.88454
2.3, -1.86753
2.31, -1.851
2.32, -1.83493
2.33, -1.81928
2.34, -1.80404
2.35, -1.78918
2.36, -1.77467
2.37, -1.7605
2.38, -1.74666
2.39, -1.73312
2.4, -1.71987
2.41, -1.70689
2.42, -1.69418
2.43, -1.68171
2.44, -1.66949
2.45, -1.65749
2.46, -1.64571
2.47, -1.63414
2.48, -1.62276
2.49, -1.61159
2.5, -1.60059
2.51, -1.58977
2.52, -1.57912
2.53, -1.56864
2.54, -1.55832
2.55, -1.54814
2.56, -1.53812
2.57, -1.52823
2.58, -1.51848
2.59, -1.50887
2.6, -1.49938
2.61, -1.49002
2.62, -1.48078
2.63, -1.47165
2.64, -1.46264
2.65, -1.45373
2.66, -1.44493
2.67, -1.43624
2.68, -1.42764
2.69, -1.41914
2.7, -1.41074
2.71, -1.40243
2.72, -1.39421
2.73, -1.38607
2.74, -1.37802
2.75, -1.37005
2.76, -1.36216
2.77, -1.35435
2.78, -1.34662
2.79, -1.33896
2.8, -1.33138
2.81, -1.32386
2.82, -1.31641
2.83, -1.30904
2.84, -1.30172
2.85, -1.29448
2.86, -1.28729
2.87, -1.28017
2.88, -1.27311
2.89, -1.26611
2.9, -1.25916
2.91, -1.25227
2.92, -1.24544
2.93, -1.23866
2.94, -1.23194
2.95, -1.22526
2.96, -1.21864
2.97, -1.21207
2.98, -1.20555
2.99, -1.19907
3, -1.19265
3.01, -1.18626
3.02, -1.17993
3.03, -1.17364
3.04, -1.16739
3.05, -1.16119
3.06, -1.15503
3.07, -1.14891
3.08, -1.14283
3.09, -1.13679
3.1, -1.13079
3.11, -1.12483
3.12, -1.1189
3.13, -1.11302
3.14, -1.10717
3.15, -1.10136
3.16, -1.09558
3.17, -1.08984
3.18, -1.08413
3.19, -1.07846
3.2, -1.07282
3.21, -1.06722
3.22, -1.06164
3.23, -1.0561
3.24, -1.05059
3.25, -1.04511
3.26, -1.03966
3.27, -1.03424
3.28, -1.02885
3.29, -1.02349
3.3, -1.01816
3.31, -1.01286
3.32, -1.00758
3.33, -1.00234
3.34, -0.99712
3.35, -0.99192
3.36, -0.98676
3.37, -0.98161
3.38, -0.9765
3.39, -0.97141
3.4, -0.96635
3.41, -0.96131
3.42, -0.95629
3.43, -0.9513
3.44, -0.94633
3.45, -0.94139
3.46, -0.93647
3.47, -0.93157
3.48, -0.9267
3.49, -0.92185
3.5, -0.91702
3.51, -0.91221
3.52, -0.90742
3.53, -0.90266
3.54, -0.89791
3.55, -0.89319
3.56, -0.88849
3.57, -0.88381
3.58, -0.87915
3.59, -0.8745
3.6, -0.86988
3.61, -0.86528
3.62, -0.86069
3.63, -0.85613
3.64, -0.85158
3.65, -0.84706
3.66, -0.84255
3.67, -0.83806
3.68, -0.83358
3.69, -0.82913
3.7, -0.82469
3.71, -0.82027
3.72, -0.81587
3.73, -0.81149
3.74, -0.80712


-------------------------------------------------

Apr 23, 2011
Equations Involving Logarithms
by: Staff


Part I

The question:

Solve for x

a) 9^(1/2x^2-1)+1=4

b) 5^(2x-1)=2^(1-x)

c) log_base 2_(x+4)+log(x-2)=4

d) log(7x-12)=2logx


The answer:

a) 9^(1/2x^2 - 1)+1=4


9^(1/2x^2 - 1) + 1 - 1 = 4 - 1

9^(1/2x^2 - 1) + 0 = 4 - 1

9^(1/2x^2 - 1) = 4 – 1

9^(1/2x^2 - 1) = 3

9^(1/2x^2 - 1) = 9^(1/2)

(1/2x^2 - 1) = (1/2)

1/2x^2 - 1 = 1/2

x^2 - 2 = 1

x^2 = 3

sqrt(x^2) = sqrt(3)

x = ±sqrt(3)


----------------------------------------------


b) 5^(2x-1)=2^(1-x)

5^(2x-1)=2^(1-x)

log5^(2x-1)=log2^(1-x)

(2x-1)*log5=(1-x)*log2

2x*log5 - log5 =1*log2 - x*log2

2x*log5 - log5 =log2 - x*log2

2x*log5 - log5 + log5 =log2 - x*log2 + log5

2x*log5 + 0 =log2 - x*log2 + log5

2x*log5 =log2 - x*log2 + log5

2x*log5 + x*log2 = log2 - x*log2 + x*log2 + log5

2x*log5 + x*log2 = log2 + 0 + log5

2x*log5 + x*log2 = log2 + log5

x*(2*log5 + log2) = log2 + log5

x*(2*log5 + log2) / (2*log5 + log2) = (log2 + log5) / (2*log5 + log2)

x*1 = (log2 + log5) / (2*log5 + log2)

x = (log5 + log2) / (2*log5 + log2)

x = 0.588592


---------------------------------------------------------


c) log_base 2_(x+4)+log(x-2)=4

log_base 2_(x+4)+log(x-2)=4

x = 6.31 using a graphical solution

log_base 2_(6.31+4)+log(6.31-2)=4

log_base 2_(10.31)+log(4.31)=4


A graphical solution was used

x = 6.31


Click the following link to view the graph. Press the Backspace key to return to this page:

http://www.solving-math-problems.com/images/graphical-solution-logarithm.png

(the table of values used to plot the graph are shown in the footnote)

---------------------------------------------------------

d) log(7x - 12)=2logx

log(7x - 12)=2logx

log(7x - 12)=log(x^2)

7x - 12 = x^2

7x – 7x -12 + 12 = x^2 - 7x + 12

0 + 0 = x^2 - 7x + 12

0 = x^2 – 7x + 12

x^2 - 7x + 12 = 0

(x - 3)*(x - 4) = 0

(x - 3) = 0

x - 3 = 0

x - 3 + 3 = 0 + 3

x - 3 + 3 = 3

x + 0 = 3

x = 3


(x - 4) = 0

x - 4 = 0

x - 4 + 4 = 0 + 4

x - 4 + 4 = 4

x + 0 = 4

x = 4


x = 3 and x = 4


Check the solutions for validity:



a) 9^(1/2x^2-1)+1=4

x = ±sqrt(3)

9^(1/2x^2 - 1)+1=4

9^(1/2 * sqrt(3)^2 - 1)+1=4

9^(1/2 * 3 - 1)+1=4

9^(3/2 - 1)+1=4

9^(.5)+1=4

3 + 1 = 4, solution valid

---------------------------------------

b) 5^(2x-1)=2^(1-x)


x = 0.588592

5^(2x-1)=2^(1-x)

5^(2*0.588592-1)=2^(1-0.588592)

1.32998 = 1.32998, solution valid

---------------------------------------


c) log_base 2_(x+4)+log(x-2)=4

x = 6.31

log_base 2_(x+4)+log(x-2)=4

log_base 2_(6.31+4)+log(6.31-2)=4

4.000 = 4, solution valid


---------------------------------------



d) log(7x - 12)=2logx

x = 3
x = 4

log(7x - 12)=2logx

for x = 3

log(7*3 - 12)=2*log(3)
0.954243 = 0.954243, solution valid

for x = 3

log(7*4 - 12)=2*log(4)
1.20412 = 1.20412, solution valid







Thanks for writing.


Staff
www.solving-math-problems.com


-------------------------------------------------


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