LOGARITMOS PROPIEDAD 1,2 Y 3

LOGARITMOS

Propiedad 1

Log A + log B

Ejemplos 1 y 2

A.B

5 3

Log 5 + log 3

.6989+ .4771 1.176 ant.

14.9468

(.7081) (3.14)

Log .7081 + log 3.14

-0.1499 + .4969

.3470 ant.

2.223

Propiedad 2

A/B Log A – log B

Ejemplos

20/5

Log 20 – log 5

1.3010 – (+ 0.6989)

1.3010-0.6989

0.6021 ant.

4

0.1523/0.4785

Log 0.1523 – log 0.4785

-0.8173 – (- 0.3201)

-0.8173 + 0.320

1 - 0.4972 ant.

0.3182

35/4.173

Log 35 – log 4.173

1.5440 – (+ 0.6204)

1.5440 – 0.6204

0.9236 ant.

8.3868

Ejemplos de propiedad 1 A.B

A.B

28.20

Log 28 + log 20

1.4471 + 1.3010

2.7481 ant.

559.8865

A.B

502.213

Log 502 + log 213

2.7007 + 2.3283

5.029 ant.

106, 905.4879

A.B

314.189

Log 314 + log 189

2.4969 + 2.2764

4.7733 ant.

59,333.5044

A.B

8.10

Log 8 + log 10

0.9030 + 1

1.9030 ant.

79.9834

A.B

81.17

Log 81 + log 17

1.9084 + 1.2304

3.1388 ant.

1,376.5753

A.B

205.141

Log 205 + log 141

2.1317 + 2.1492

4.4609 ant.

28,900. 14355

A.B

7.5

Log 7 + log 5

0.8450 + 0.6989

1.5439 ant.

34.9864

A.B

13.16

Log 13 + log 16

1.1139 + 1.2041

2.318 ant.

207.9696

A.B

19.2

Log 19 + log 2

1.2787 + 0.3010

1.5797 ant.

37.9926

A.B

3.4

Log 3 + log 4

0.4771 + 0.6020

1.0791 ant.

11.9977

Ejemplos propiedad 1 (con decimales)

A.B

(.4791) (1.8252)

Log .4791 + log 1.8252

-0.3195 + 0.2613

-0.0582 ant.

0.8745

A.B

(.2243) (.1763)

Log .2243 + log .1763

-0.6491 + (-0.7537)

-0.6491-0.7537

-1.4028 ant.

0.03955

A.B

(1.1326) (.4995)

Log 1.1326 + log .4995

0.0540 + (-0.3014)

0.0540 - 0.3014

-0.2474 ant.

0.5657

A.B

(.9666) (.8492)

Log .9666 + log .8492

-0.0147 + (-0.0709)

-0.0147 – 0.0709

-0.0856 ant.

0.8211

A.B

(.7259)(.6358)

Log .7259 + log .6358

-0.1391 + (-0.1966)

-0.1391 – 0.1966

-0.3357 ant.

0.4616

A.B

(.5211) (.4999)

Log .5211 + log .4999

-0.1391 + (-0.3011)

-0.1391-0.3011

-0.5841 ant.

0.2605

A.B

(0.3781) (0.2477)

Log 0.3781 + log 0.2477

-0.4223 + (-0.6060)

-0.4223-0.6060

-1.0283 ant.

0.0936

A.B

(0.1800) (1.4297)

Log 0.1800 + log 1.4297

-0.7447 + 0.1552

-5.895 ant.

0.2573

A.B

(2.9833) (3.3333)

Log 2.9833 + log 3.3333

0.4746 + 0.5228

0.9974 ant.

9.9403

A.B

(4.192) (5.2837)

Log 4.192 + log 5.2837

o.6148 + 0.7232

1.338 ant.

21.7770

Propiedad 2 A/B ejemplos

Log A – log B

28/11

Log 28 – log 11

1.4471 – 1.0413

0.4058 ant.

2.5456

54/33

Log 54 – log 33

1.7323 – 1.5185

0.2138 ant.

1.6360

38/7

Log 38 – log 7

1.5797 – 0.8450

0.7347 ant.

5.4287

73/12

Log 73 – log 12

1.8633 – 1.0791

0.7842 ant.

6.0841

95/53

Log 95 – log 53

1.9777 + 1.7242

0.2535 ant.

1.7926

352/189

Log 352 – log 189

2.5465 – 2.2764

0.2701 ant.

1.8625

8/3

Log 8 – log 3

0.9030 + 0.4771

0.4259 ant.

2.6662

10/5

Log 10 – log 5

1- 0.7781

0.2219 ant.

1.6668

311/206

Log 311- log 206

2.4927- 2.3138

0.1789ant.

1.5097

598/319

Log 598 – log 319

2.7767 – 2.5037

0.273 ant.

1.8749

Ejemplos de propiedad 2 (con punto decimal)

0.1892/0.1050

Log 1892 – log 0.1050

-0.7230 – 0.9788

0.2558 ant.

1.8021

0.5934/0.9321

Log 5934 – log 0.9321

-0.2266 – (-0.0305)

-0.2266+0.0305

-0.1961 ant.

0.6366

0.8572/0.1233

Log 0.8572 – log 0.1233

-0.0669- (-0.9090)

-0.0669+0.9090

0.8421 ant.

6.9551

7.1241/2.2359

Log 7.1241 – log 2.2359

0.8527 – 0.3494

0.5033 ant.

3.1863

3.5091/1.9221

Log 3.5091- log 1.9221

0.5451-0.2837

0.2614ant.

1.8255

5.1111/2.3872

Log 5.1111 – log 2.3872

0.7085 – 0.3778

0.3307 ant.

2.1414

8.2489/0.1588

Log 8.2489 – log 0.1588

0.9163- (-0.7991)

0.9163+0.7991

1.7154 ant.

51.9378

9.2913/3.5810

Log 9.2913 – log 3.5810

0.9680- 0.5540

0.414 ant.

2.5941

1.7777/0.2340

Log 1.7777 – log 0.2340

0.2498- (-0.6307)

0.2498+0.6307

0.8805 ant.

7.5945

0.1920/0.2110

Log 0.1920 – log 0.2110

-0.7166 – (-0.6757)

-0.7166+0.6757

-0.0409 ant.

0.9101

Ejemplos de propiedad 2 (con punto decimal y entero)

54/5.123

Log 54 – log 5.123

1.7323 – 0.7095

1.0228 ant.

10.5390

89/1.982

Log 89 – log 1.982

1.9493 – 0.2971

1.6522 ant.

44.8952

72/3.541

Log 72 – log 3.541

1.8573 – 0.5491

1.3082 ant.

20.3329

22/1.822

Log 22 – log 1.822

1.3424 – 0.2605

1.0819 ant.

12.0753

15/2.734

Log 15 – log 2.734

1.1760 – 0.4367

0.7393 ant.

5.4865

37/4.128

Log 37 – log 4.128

1.5682 – 0.6157

0.9525 ant.

8.9639

45/6.882

Log 45 – log 6.882

1.6532- 0.8377

0.8155 ant.

6.5388

63/7.519

Log 63 – log 7.519

1.7993 – 0.8761

0.9232 ant.

8.3791

99/8.765

Log 99 – log 8.765

1.9956-0.9427

1.0529 ant.

11.2953

16/9.118

Log 16 – log 9.118

1.2041 – 0.9598

0.2443 ant.

1.7550

Propiedad 3

a^b B log A

Ejemplo 1

4^3

3 log 4

3 (.6020)

1.8060 ant.

63.4734

Ejemplo 2

〖5 〗_5^3

3/5 log⁡〖5 〗

3/5 (.6989)

.4190 ant.

2.6265

Ejemplo 3

〖3/7 〗_6^1

1/6 〖(log〗⁡〖3/7) 〗

1/6 log⁡(.4285)

1/6 (-.3679)

- .0613 ant.

.8683

Ejemplo 1 ejercicios

8^2

2 log⁡〖8 〗

2 (0.9030)

1.8061 ant.

63.9882

〖15〗^6

6 log⁡〖8 〗

6 (1.1760)

7.0565 ant.

11, 390,625.

〖23〗^10

10 log⁡〖23 〗

10 (1.3617)

13.617 ant.

4.1399

〖87〗^7

7 log⁡87

7 (1.9395)

13.5766 ant.

3.7725

2^2

2 log⁡〖2 〗

2 (0.3010)

0.6020 ant.

4

7^9

9 log⁡〖7 〗

9 (0.8450)

7.6058 ant.

40, 353, 607.

〖205〗^16

16 log⁡205

16 (2.3117)

36.9880 ant.

9.7288

〖36〗^11

11 log⁡〖 36 〗

11 (1.5563)

17.1193 ant.

1.3161

〖27 〗^(6 )

6 log⁡〖27 〗

6 (1.4313)

8.5881 ant.

387, 420, 489.

〖48〗^3

3 log⁡48

3 (1.6812)

5.0437 ant.

110, 592.

〖55〗^9

9 log⁡〖55 〗

9 (1.7403)

15.6632 ant.

4.6053

9^2

2 log⁡〖9 〗

2 (0.9542)

1.9084 ant.

81

5^8

8 log⁡〖5 〗

8 (0.6989)

5.5917 ant.

390, 625

〖311〗^5

5 log⁡〖311 〗

5 (2.4927)

12.4638 ant.

2.9093

〖18〗^12

12 log⁡18

12 (1.2552)

15.0632 ant.

1.1568

Ejemplo 2 ejercicios

6_3^2

2/3 log⁡〖6 〗

2/3 (0.7781)

0.5187 ant.

3.3019

〖12〗_9^8

8/9 log⁡〖12 〗

8/9 (1.0791)

0.9592 ant.

9.1048

3_3^3

3/3 log⁡〖3 〗

3/3 (0.4771)

0.4771 ant.

3

9_7^1

1/7 log⁡9

1/7 (0.9542)

0.1363 ant.

1.3687

〖26〗_2^9

2/9 log 26

2/9 (1.4149)

6.3673 ant.

2, 330, 129. 541

2_2^4

4/2 log⁡〖2 〗

4/2 (0.3010)

0.6020 ant.

4

1_8^5

5/8 log⁡〖1 〗

5/8 (0)

0 ant.

1

〖15〗_3^6

6/3 log⁡〖15 〗

6/3 (1.1760)

2.3521 ant.

225

4_6^7

7/6 log 9

7/6 (0.6989)

0.8154 ant.

6.5383

5_8^6

6/8 log⁡5

6/8 (0.6989)

0.5242 ant.

3.3437

7_8^12

12/8 log⁡〖7 〗

12/8 (0.8450)

1.2676 ant.

18.5202

8_11^10

10/11 log⁡〖8 〗

10/11 (0.9030)

0.8209 ant.

6.6220

〖10〗_2^5

5/2 log 10

5/2 (1)

2.5 ant.

316.2277

〖22〗_2^2

2/2 log⁡〖22 〗

2/2 (1.3424)

1.3424 ant.

22

〖38〗_2^6

6/2 log⁡〖38 〗

6/2 (1.5797)

4.7393 ant.

54,872

Ejemplo 3 ejercicios

〖8/7〗_3^2

2/3 ( log⁡〖8/7) 〗

2/3 log⁡(1.1428)

2/3 (0.0579)

0.0386 ant.

1.0930

〖6/4〗_3^7

7/3 log⁡〖6/4 〗

7/3 log (1.5)

7/3 (0.1760)

0.4108 ant.

2.5756

〖1/3〗_4^5

5/4 log⁡〖1/3 〗

5/4 log (0.3333)

5/4 (-0.4771)

-0.5964 ant.

0.2532

〖2/7〗_5^1

1/5 log⁡〖2/7 〗

1/5 log (0.2857)

1/5 (-0.5440)

-0.1088 ant.

0.7783

〖5/8〗_2^(9 )

9/2 log⁡〖5/8 〗

9/2 log (0.625)

9/2 (-0.2041)

-0.9185 ant.

0.1206

〖3/2〗_3^5

5/3 log⁡〖3/2 〗

5/3 log (1.6666)

5/3 (0.2218)

0.3697 ant.

2.3427

〖4/8〗_5^9

9/5 log⁡〖4/8 〗

9/5 log (0.5)

9/5 (-0.3010)

-0.5418 ant.

0.2871

〖7/2〗_1^3

3/1 log⁡〖7/2 〗

3/1 log (3.5)

3/1 (0.5440)

1.6322 ant.

42.875

〖9/3〗_10^12

12/10 log⁡〖9/3 〗

12/10 log (3)

12/10 (0.4771)

0.5725 ant.

3.7371

〖10/3〗_1^10

10/1 log⁡〖10/3 〗

10/1 log (3.3333)

10/1 (0.5228)

1.7429 ant.

55.3241

〖15/8〗_7^2

2/7 log⁡〖15/8 〗

2/7 log (1.875)

2/7 (0.2730)

0.0780 ant.

1.1967

〖12/10〗_2^8

8/2 log⁡〖12/10 〗

8/2 log (1.2)

8/2 (0.0791)

0.3167 ant.

2.0736

〖28/2〗_5^1

1/5 log 28/2

1/5 log (14)

1/5 (1.1961)

0.2292 ant.

1.6952

〖11/3〗_2^5

5/2 log⁡〖11/3 〗

5/2 log (3.6666)

5/2 (0.5642)

1.4106 ant.

25.7429

〖8/5〗_2^1

1/2 log⁡〖8/5 〗

½ log (1.6)

½ (0.2041)

0.1020 ant.

1.2649

Ejercicio 298 del libro de algebra

532x0.184

Log 532 + log 0.184

2.7259 + (-0.7351)

2.7259-0.7351

1.9908 ant.

97.9039

191.7 x 432

Log 191.7 + log 432

2.2826 + 2.6354

4.918 ant.

82, 794.21637

0.7 x 0.013 x 0.9

Log 0.7 + log 0.013 + log 0.9

-0.1549 + (-1.8860) + (- 0.0457)

-0.1549 – 1.8860 – 0.0457

-2.0866 ant.

0.0081

7.5 x 8.16 x 0.35 x 10037

Log 7.5 + log 8.16 + log 0.35 + log 10037

0.8750 + 0.9116 + (-0.4559) + 4.0016

0.8750 + 0.9116 – 0.4559 + 4.0016

5.3323 ant.

214, 931.4655

3.2 x 4.3 x 7.8 x 103.4 x 0.019

Log 3.2 + log 4.3 + log 7.8 + log 103.4 + log 0.019

0.5051 + 0.6334+ 0.8920 + 2.0145 + (-1.7212)

0.5051 + 0.6334 + 0.8920 + 2.0145 – 1.7212

2.3238 ant.

210.7657

95.13 ÷ 7.23

Log 95.13 – log 7.23

1.9783 – 0.8591

1.1192 ant.

13.1583

8.125 ÷ 0.9324

Log 8.125 – log 0.9324

0.9097 – (-0.0303)

0.9097+ 0.0303

0.94 ant.

8.7096

7653.95÷12.354

Log 7653.95 – log 12.354

3.8838 – 1.0918

2.792 ant.

619. 4410

0.72183/0.0095

log 0.72183 – log 0.0095

-0.1415 – (- 2.0222)

-0.1415 + 2.0222

1.8807 ant.

75.9801

9114/0.02

Log 9114 – log 0.02

3.9597 – (-1.6989)

3.9597 + 1.6989

5.6586 ant.

455,617.0838

2^10

10 log⁡〖2 〗

10 (0.3010)

3.0102 ant.

1,024

〖0.15〗^3

3 log⁡〖0.15 〗

3 (-0.8239)

-2.4717 ant.

0.0033

〖18.65〗^4

4 log⁡18.65

4 (1.2706)

5.0827 ant.

120, 980. 4915

〖00.84〗^2

2 log⁡00.84

2 (-0.0757)

-0.1514 ant.

0.7056

〖7.2〗^6

6 log⁡〖7.2 〗

6 (0.8573)

5.1439 ant.

139, 314. 0695

√3

3^1

1 log⁡〖3 〗

1 (0.4771)

.4771 ant.

3

3√2

2_3^1

1/3 log⁡〖2 〗

1/3 (.3010)

0.1505 ant.

1.414

4√5

5_4^1

1/4 log⁡〖5 〗

1/4 (.6989)

0.1747 ant.

1.4953

5√63

6_5^3

1/5 log⁡〖6 3〗

1/5 (1.79)

0.3598 ant.

2.2901

7√815

〖815〗_7^1

1/15 log⁡815

1/5 (2.9111)

.4158 ant.

2.6054