8º Semana

  1.-5^x=.17

x log 5=log .17

x= log .17 / log 5

x =-.7695/ .6989

x=-1.1010

2.- .18 ^x=3.16

x log .18 = log 3.16

x= log 3.16 / log .18

x= .4996/-.7447

x= - .6708

3.-2.5 ^2x=4

(2x) log 2.5 = log 4

2x= log 4/ log 2.5

2x= .6020/.3979

2x=1.5129/2

x=.75645

4.-9 ^x=8

x log 9 = log 8

x= log 8 / log 9

x= .9030 / .9542

x= .9463

5.-1.5^{5 x}=5.5

(5x) log 1.5 = log 5.5

5x=  log 5.5 / log 1.5

5x= .7403/.1760

5x=4.2062

x=4.2062/5

x=.84125

6.-3^{3 x}=9

3x log 3 = log 9

3x =  log 9 / log 3

3x = .9542 / .4771 =2

x= 2/3 .6666

7.-3^2x+5=5

(2x+5) log 3 = log 5

2x+5 = log 5 / log 3

2x+5.6989/.4771

2x+5=1.4648

2x=1.4648 – 5

x= -3.5351 /2

x= -1.5351

8.-2.5^2x-2=10

(2x-2) log 2.5 = log 10

2x-2 = log 10 / log 2.5

2x2= 1 / .3979

2x-2=2.5131 +2

x=4.5131/2

x=2.2565

9.-9^5x-3=6

(5x^-3) log 9 = log 6

5x ^-3 = log 6 /  log 9

5x^-3= .7781/.9542

5x^-3=.8154

5x=.8154 + 3

x= 3.8154 / 5

x= .7630

10.-3.5^3x-1=2.5

(3x-1) log 3.5 = log 2.5

3x^-1= log 2.5 / log 3.5

3x^-1 =.3979/.5440

3x^-1=.7314+1

x=1.7314/3

x=.5771

11.-3^x=20

x log 3= log 20

x= log 20/ log 3

x=1.3010/.4771

x=2.7268

12.-2^5x=.97

5x= log 2 = log .97

5x= log 2 / log .97

5x= .3010 / -.0132

x=-22.8030 /5

x=-4.5606

13.-3.5^7x-1/.87

(7x^-1) 3.5 log = .87 log

7x^-1  = log .87 / log 3.5

7x-1 = -.0604/.5440

7x=-.1110 +1

x= .8889 /7

x= .1269

14.-.97^2x=.56

(2x) log .97 = log .56

2x log .56 / log .97

2x=-.2518 / -.0132

2x= 19.0757

x= 19.0757 / 2

x= 9.5378

15.-2^3x=.89

(3x) log 2 = log.82

3x = .82 log / 2 log

3x -.0861/.3010

3x= -2.6780

x= -2.6780/ 3

x=-.8926

1.-2^7x+1=7

(7x+1) 2 log =7 log

7x+1 log 7 / log 2

7x+1 .8450/.3010

7x=2.8073 -1

x=1.8073/7

x=.2581

2.-2^.7x=.7

(.7x) log 2 = log .7

.7 = log .7 / log 2

.7=  -.1549/.3010

.7=-.5146

-.5146/.7

x= -.7361

3.-.2^2x=.5

(2x) log .2 = log .5

2x= log .5 / log .2

2x=-.3010/-.6989

x=.4306/2

x=.2153

4.-3.5^x=3.6

x= log 3.5 = log 3.6

x= log 3.6 / log 3.5

x= .5563 / .5440

x=1.0226

5.-3^2x=10.5

2x log 3= log 10.5

2x= log 10.5 / log 3

2x= 1.0211/.4771

x= 2.1402/2

x=1.0701

6.-9^7x-10=1

(7x-10) log 9 = log 1

7x-10 log 1 / log 9

7x-10 = 0/.9542

7x=0+10

x=10/7

x=1.4285

7.-4.6^x=35

x log 9.6 = log 35

x= log 35 / log 4.6

x=1.5440/.6627

x=2.3298

8.-5^3x=.58

3x log 5 = log.58

3x= log .58/ log 5

3x=-.2365/.6989

x=-.3383/3

x= -.1127

9.-2.3^5x-1=.9

(5x^-1) 2.3 log=.9 log

5x^-1 log.9 / log 2.3

5x^-1 =-.0457/.3617

5x=-.1263 + 1

x= .8935/5

x=.1747

10.-2^x=27

x log 2 = log 27

x= log 27/ log 2

x= 1.4313/ .3010

x=4.7551

1)      .8^x=2.2

x  log .8 = log 2.2

x= log 2.2/ log.8

x= .3424/-.0969

x=-3.5335

2)      .17^x=.7

x  log .17 = log .7

x= log.7/ log.17

x/-.1549/-.7695

x=2012

3)      (3/2)^x=3/2

x log 3/2 = log 3/2

x= log 3/2 / log 3/2

x=.1760/.1760

x=1

4)      .56^x=.97

x  log .56 = log.97

x= log .97/ log.56

x=-0.0132/-.2518

x=.0524

5)      .8^x=2.3

x  log .8 = log 2.3

x= log 2.3 / log .8

x=.3617/-.0969

x=-3.7327

6)      .25 ^3/2x=.5

(3/2x) log .25= log.5

3/2x= log .5 /.25

3/2x=-.3010/-.6020

x=.5/3/2

x=.3333

7)      3.6 ^1.7x=.8

1.7x = log 3.6 = log.8

1.7x= log.8/ log3.6

1.7x=-.0969/.5563

x=-.1741/1.7

x=-.1024

8)      1.5^3x=2.5

(3x) log 1.5= log2.5

3x= log2.5/ log1.5

3x=.3979/.1760

x/2.2607/3

x=.7535

9)      2.3 ^5/2=5

(5/2x) log 2.3 = log 5

5/2 = log 5 / log 2.3

5/2=.6989/.3617

x=1.9322/5.2

x=.7729

10)   2^2/3x=4/5

(2/3) log 2 = log 4/5

2/3= log4/3/ log2

2/3=-.0969.3010

x=-.3219/2/3

x=-.4828

11)   7^x+6=5

(x+6) log 7 = log 5

x+6= log5/ log7

x+6=.6989/.8450

x=.8271+6

x=6.8271

12)   28^2x-7=3

(2x-7) log 8 = log3

(2x-7) log 3 / log 8

(2x-7).4771/.9030

2x=.5283+7

x=7.5283/2

x=3.7641

13)   4^3x-5=2

(3x-5) log4= log2

(3x-5)= log2/ log4

3x-5=.3010/.6020

3x=.5+5

x=5.5/3

x=1.8333

14)   3^1/2x-2=.75

(1/2 x-2) log3= log7.5

(1/2x-2) log.75/ log3

1/2x-2=-.1249/.4771

1/2x=-.2617+2

x=1.7382/1/2

x=3.4764

15)   9^{3/2 + ½}=1.5

(3/2x1/2) log9= log1.5

3/2x1/2= log1.5/ log9

3/2x1/2=1.1760/.9542

3/2x=1.2324+1/2

x=1.7324

x=1.1549

1)      4^3x+7-2x=36

(x+7) log 4 = log 36

x+7(log 367 log4

x+7=1.5563/.6020

x=2.5852-7

x=-4.4147/1

x=-4.4147

2)      3^2/3x=4

(2/3) log3 = log 4

(2/3x) log 4 = log 3

2/3x0.6020/.4771

x=1.2617/3/2

x=.8411

3)      2^7x-3-2x+6=10

(5x+3) log 2_= log

5x+3 = log 10 / log 2

5x+3=1/.3010

5x=3.3222 – 3

x=.3222/5

x=.6044

4)      5.7^2/3-7

(2/3x7) log 5.7 = log .67

2/3-7= log.67/ log5.7

2/3-7=-.1739/.7558

5)      2.3^.5x-2=.7

(.5x-2) log 2.3 = .7

.5x-2= log.7/ log2

.5x-2=-.1549/.3010

.5x=-.1546+2

x=1.4853/.5

x=2.9707

6)      3.7^2x-3+7x-1=2

(9x-4) log 3.7 = log 2

(9x-4) = log2/ log3.7

(9x-4)=.3010/.5682

9x=.5297+4

x=4.5297+9

x=.5033

7)      2.5^{1/2 x}=9

(1/2x) log 2.5= log9

1/2x)= log .9 /2.5

(1/2)=-.0457/.3979

x=-.1148/1/2

x-.2297

8)      3.2 ^7x-3=19

(7x-3) log 3.2 = log 19

(7x-3)=log19/log3.2

(7x-3)=1.2787/.5051

7x=.5517/3

x=3.5517/7

x=.5073

9)      4^3x-7=2.4

(3x-7) log 4 = log 2.4

(3x-7) = log 2.4 / log 4

(3x-7) =.3802/.6020

3x=.6315+7

x=7.6315/3

x=2.5438

10)   1.5^6x-3=4.7

(6x-3) log 1.5 = log 4.7

(6x-3)= log4.7/log1.5

(6x-3)=.6720/.1760

6x=3.8181+3

x=6.8181/6

x=1.1363

Problemas del libro de Baldor

 1.-532 X 0.184

log 532 + log .184

2.7259 + (-.7551)

1.9907 ANT

97.888

2.-191.7 X 432

log 191.7 + log 432

2.2826 + 2.6354

4.9181 ANT

82814.4

3.-0.7 X 0.013 X 0.9

log .7 + log 0.03 + log .9

.8450 – 1.8860 - .0457

-1.0867 ANT

.0819

4.-7.5 X 8.16 X 0.35 X 10037

log 7.5 + log 8.16 + log .35 + log 10037

.8450+.9116-.4559+4.0016

5.3323 ANT

214931.4635

5.-3.2 X 4.3 X 7.8 103.4 X 0.019

log  .5051 + log .6334 + log .8920 + log 2.0145

-1.7212

2.3238 ANT

210.7657

6.-95.13/7.23

log 95.13 – log 7.23

1.9783 - .8591

1.9743 ANT

94.2708

7.-8.125/0.9324

log 8.125 – log 9324

.9098 + .0303

.9401 ANT

8.7116

8.-7653.95/12.354

log 7653 – log 12.354

3.8838 – 1.0918

2.792 ANT

619.4410

9.-0.72183/0.0095

log .72183 – log .0095

-.1415 + 2.0222

1.8807 ANT

75.9801

10.-9114/0.02

log 9114 – log .02

3.9597 + 1.6987

5.6584 ANT

455407.3127

11.-2¹⁰

10 log 2

10 (.3010)

3.0102 ANT

1024

12.-0.15³

3 log .15

3 (-.8239)

-2.4717 ANT

3.375 X 10^-3

13.-18.65⁴

4 log 18.65

4 (1.2706)

5.0827 ANT

120980.4915

14.-00.84²

2 log .84

2 (-.0757)

-.1514 ANT

.7056

15.-7.2⁶

6 log 7.2

6 (.8573)

5.1439 ANT

139314.0695

16.-√3

½ log 3

½ (.4771)

.2385 ANT

1.7320

17.-³√2

1/3 log 2

1/3 (.3010)

.1003 ANT

1.2599

18.-⁴√5

¼ log 63

¼ (1.7993)

.4498 ANT

2.8173

19.-⁵√63

¼ log 5

¼ (.6989)

.1747 ANT

1.4953

20.-⁷√815

1/7  log 815

1/7 (2.91115)

.4158 ANT

2.6054

3º Propiedad

1.- 3²

 2 log  

2 . (.4771)

.9542 ANT

9

2.- 4³

3 log 4

3 (.6020)

1.8061 ANT

64

3.-5⁴

4 log 5

4 (.6989)

2.7958

625

4.-6⁵

5 log 6

5(.7781

5.-7⁶ 

6 log 7

6 (.8450)

5.0705 ANT

1.7649

6.-8⁷

7 log 8

7 (.9030)

6.3216 ANT

2097152

7.-9⁸

8  log 9

8 (.9542)

7.6339 ANT

43046721

8.-7³

3 log 7

3 (.8450)

2.5352 ANT

343

9.-14²

 2 log 14

2 (1.1461)

2.2922 ANT

196

10.-15³

3 log 15

3 (1.1760)

3.5282 ANT

3375

11.-2⁸

8 log 2

8 (.3010)

2.4082 ANT

256

12.-18⁴

4 log 18

4 (1.2552)

5.0210 ANT

104976

13.-23⁴

4 log 23

4 (1.3617)

5.4469 ANT

279841

14.-3⁹

9 log 3

9(.4771)

4.2940 ANT

19682

15.-20³

3 log 20

3 (1.3010)

3.9030 ANT

8000

16.- 2 ½

½ log 2

½ (.3010)

.1505 ANT

1.4142

17.- 3 ^1/3

1/3 log 3

1/3 (.4771)

.1590 ANT

1.4422

18.-4 ^1/4

1/4 log 4

¼ (.6020)

.1505 ANT

1.4142

19.- 5 ^2/5

2/5 log 5

2/5 (.6989)

.2795 ANT

1.9036

20.-6 ^3/7

3/7 log 6

3/7 (.7781)

.3334 ANT

2.1552

21.-7 ^4/8

4/8 log 7

4/8 (.8450)

.4225 ANT

2.6457

22.- 8 ^1/9

1/9 log 8

1/9 (.9030)

.1003 ANT

1.2599

23.-12 ¾

3/4  log 12

3/4 (1.0791)

.8093 ANT

6.4474

24.-17 ^1/9

1/9 log 17

1/9 (1.2304)

.1367 ANT

1.3699

25.-14 ^1/8

1/8 log 14

1/8 (1.1461)

.1432 ANT

1.3908

26.-9 ^6/3

6/3 log 9

6/3 (.9542)

1.9084 ANT

81

27.-23 ^2/2

2/2 log 23

2/2 (1.3617)

1.3617 ANT

23

28.-11 ^19/21

19/21 log 11

19/21 (1.0413)

.9422 ANT

8.7541

29.-8 ^1/5

1/5 log 8

1/5 (.9030)

.1806 ANT

1.5157

30.-10 ^8/4

8/4 log 10

8/4 (1)

2 ANT

100

31.-6/8 ^3/6

3/6 log .75

3/6 (-0.1249)

-0.0624 ANT

0.8660

32.-12/15 ^7/8

7/8 log .8

7/8 (-.0969)

-0.0847 ANT

.8226

33.-3/4 ^3/8

3/8 log ¾

3/8 (.75)

.28125 ANT

1.9109

34.-17/5 ^2/9

2/9 log 17/5

2/9 (.5314)

.1181 ANT

1.3125

35.-17/12 ½

½ log 17/12

½ (.1512)

.0756 ANT

1.1902

36.-1/3 ^17/8

17/8 log 1/3

17/8 (-.4771)

.7083 ANT

5.1089

37.-23/56 ^8/9

8/9 log 23/56

8/9 (.4107)

0.3650

2.3178

38.-75/12 ½

½ log 75/12

½ (6.25)

3.125 ANT

1333.52

39.-23/24 ^6/2

6/2 log 23/24

6/2 (.9583)

2.875 ANT

749.842

40.-13/68 ^13/16

13/16 log13/68

13/16 (.1911)

.1553 ANT

1.4293

41.-1/2 ^1/3

1/3 log ½

1/3 (-0.3010)

-0.10034 ANT

0.7937

42.-41/60 ^3/7

3/7 log 41/60

3/7 (.6833)

.2928 ANT

1.9627

43.-21/19 ^67/35

67/35 log 21/19

67/35 (1.1052)

2.1157 ANT

130.5537

44.-1/9 ^1/3

1/3 log 1/9

1/3 (.11)

0.0370 ANT

1.0890

45.-3/4 6/7

6/7  log ¾

6/7 (.75)

.6428 ANT

4.3939

2º Propiedad

1.-  4/2

log 4 – log 2

.6020 - .3010

.301 ANT

1.999

2.- 6/4

log 6 – log 4

0.7781 – 0.6020

0.1761 ANT

1.5000

3.- 8/6

log 8  – log 6

0.9030 – 0.7781

0.1249 ANT

1.3332

4.- 12/4

log 12  – log 4

1.0791 – 0.6020

0.4771 ANT

2.9998

5.- 18/2

log 18 – log 2

1.2552 – 0.3010

0.9542 ANT

8.9991

6.- 30/6

log 30 – log 6

1.4771 – 0.7781

0.699 ANT

5.0003

7.- 42/6

log 42  – log  6

1.6232 – 0.7781

0.8451 ANT

7.0000

8.- 16/7

log  16 – log 7

1.2041 – 0.8450

0.3591 ANT

2.2861

9.- 21/8

log  21 – log 8

1.3222 – 0.9030

0.4192 ANT

2.6254

10.- 5/19

log 15 – log 19

1.1760 – 1.2787

-0.1027 ANT

0.7894

11.- .1316/.0106

log .1316  – log .0103

-0.8807 + 1.9871

1.1064 ANT

12.777

12.-  .0681/.1316

log .0681 – log .1316

-1.1668 + 0.1316

-1.0352 ANT

0.0922

13.- .1618/.1920

log .1618  – log .1920

-0.7910 + 0.7166

-0.0744 ANT

0.8425

14.- .2122/.2324

log  .2122 – log .2324

-0.6732 + 0.6337

-0.0395 ANT

0.91302

15.-.  6762/.6160

log .6762 – log .6160

-0.1699 + 0.2104

0.0405 ANT

1.0977

16.-   .5248/.4443

log .5248  – log .4443

-0.2500 + 0.3523

0.0723 ANT

1.1811

17.-  .4240/.3938

log .4240 – log .3938

-0.3726 + 0.4047

0.0321 ANT

1.0767

18.-  .3633/.3027

log .3633 – log .3027

-0.4397 + 0.7164

0.2767 ANT

1.8910

19.-  .2423/.1921

log .2423 – log .1921

-0.6156 + 0.7164

0.1008 ANT

1.2612

20.- .6719/.2133

log .6719 – log .2133

-0.1726 + 0.6710

0.4984

3.1506

21.- 4/3.5231

log 4 – log 3.523

0.6020 – 0.5469

0.0551 ANT

1.1352

22.- 37/18.520

log  37 – log 18.520

1.5682 -1.2552

0.313 ANT

2.0558

23.-10/3.123

log 10   – log 3.123

1 - .4945

0.5055 ANT

0.5055

24.- 55/12.999

log 55   – log  12.999

1.7403 – 1.1139

0.6264 ANT

4.2305

25.-23/1.367

log 23  – log 1.367

1.3617 -.1357

1.226 ANT

16.8267

26.-81/.3167

log 81  – log .3167

1.9084 + 0.4993

2.4077 ANT

255.681

27.-6/1.671

log 6   – log 1.671

.7781 - .2229

.5552 ANT

3.5908

8.- 94/14.009

log 94   –  log 14.009

1.9731 – 1.1464

0.8267 ANT

6.7096

29.-28/6.486

log 28   – log 6.486

1.4471 – 0.8119

0.6352 ANT

4.3171

30.-6/12.216

log  6 – log 12.216

0.7781  1.0869

-0.3088 ANT

0.4911