Logaritmos

Logaritmos

Propiedad 3

B log A

Ejemplo 1:

3 log 4
3(.6020)
1.8060 ANT.
r=63.9734

Ejemplo 2:

3/5 log 5
3/5(.6989)
.4190 ANT.
r= 2.6265

Ejemplo 3:

(3/7) 1/6

1/6 (log 3/7)
1/6 log (.4285)
1/6(-.3680)
-.0613 ANT.
r=0.8683

Ejercicios1

Propiedad 1

1.-  8³3 log 8
3(0.9030)
2.7092 ANT.
r=511.9175

2.-  7²
2 log 7
2(.8450)
1.6001 ANT.
r=39.8198

3.- 
4 log 6
4(.7781)
12.4504 ANT.
r=2.8209

4.- 3²2 log 3
2(.8450)
1.6001 ANT.
r=39.8198

5.-
5 log 6
5(.7781)
3.8907 ANT.
r=7774.9928

6.-5³3 log 5
3(0.6989)
2.0969 ANT.
r=124.9971

7.- 4²2 log 4
2(.6020)
1.2041 ANT.
r=15.9992

8.- 3³3 log 3
3(0.4771)
1.4313 ANT.
r=26.9960

9.-
5 log 4
5(.6020)
3.0102 ANT.
r=1023.7643

10.-
4 log 2
4(.3010)
1.2041 ANT.
r=15.9992

11.- 
6 log 2
6(.3010)
1.8061 ANT.
r=63.9882

12.- 8²2 log 8
2(.9030)
1.8061 ANT.
r=63.9882

13.-
8 log 5
8(0.6989)
5.5917 ANT.
r=390571.0057

14.-
4 log 7
4(.8450)
3.3803
r=2400.4905

15.-
6 log 8
6(.9030)
5.4185 ANT.
r=262119.9039

Ejercicio 2

1.-
1/3 log 3
1/3(0.4771)
0.1590 ANT.
r=1.4421

2.-
½ log 8
½ (.9030)
.4515 ANT.
r=2.8281

3.-
¼ log 5
¼(.6989)
0.1747 ANT.
r=1.4952

4.- 
¾ log 8
¾ (.9030)
0.6773 ANT.
r= 4.7566

5.-
3/5 log 9
3/5(.9542)
50.5725 ANT.
r=1.5097

6.- 2 ½ ½ log 2
½ (.3010)
.1505 ANT.
r=1.4141

7.-
3/8 log 3
3/8 (.4771)
80.1789 ANT.
r= 1.5097

8.-
5/4 log 8
5/4(.9030)
.1505 ANT.
r=1.4141

9.-7 ¾ ¾ log 7
¾ (.8450)
.6338 ANT.
r=4.3032

10.-
7/3 log 3
7/3 (.4771)
1.1132 NT.
r=12.9777

11.-  9 ½ ½  log 9
½ (.9542)
.4771 ANT.
r=2.9998

12.-
9/3 log 7
9/3 (.8450)
2.5352 ANT.
r=342.9256

13.-6 ¾ ¾ log 6
¾ (0.7781)
0.5836 ANT.
r=3.8335

14.-
4/6 log 5
4/6 (.6989)
.4659 ANT.
r=2.9234

15.-
3/7 log 4
3/7 (.6020)
.2580 ANT.
r=1.8113

Ejercicio 3

1.- (¾) ½ ½(log ¾)
½ log (.75)
½ (-0.1249)
-0.0624 ANT.
r=0.8661

2.- (2/4) 3/53/5(log 2/4)
3/5 log (.5)
3/5 (-.03010)
-0.1806 ANT.
r=0.6597

3.- (3/5) 1/81/8(log 3/5)
1/8 log (.6)
1/8 (-0.2218)
-0.0277 ANT.
r=0.9382

4.- (3/5) ½ ½ (log 3/5)
½ log (.6)
½ (-0.2218)
-0.1109 ANT.
r=0.7746

5.- (9/4) 3/53/5 (log 9/4)
3/5 log (2.25)
3/5 (0.3521)
0.2113 ANT.
r=1.6266

6.-  (4/7) 4/44/4 (log 4/7)
4/4 log (0.5714)
4/4 (-0.2430)
-0.0607 ANT.
r=0.8694

7.- (9/3) ½ ½ (log 9/3)
½ log (3)
.75 ANT.
r=5.6234

8.-  (8/4) ¾ ¾ (log 8/4)
¾ log (2)
¾ (0.4771)
.357 ANT.
r=2.2750

9.- (3/7) 5/45/4 (log 3/7)
5/4 log (.4285)
-0.3680 ANT.
r=0.4285

10.- (8/3) 2/32/3 (log 8/3)
2/3 log (8/3)
2/3 log (2.66)
0.4248 ANT.
r=2.6595

11.- (3/8) ½ ½ (log 3/8)
½ log (.375)
-0.4259 ANT.
r=0.3750

12.- (2/4) 7/87/8 (log 2/4)
7/8 log (.5)
7/8 (-0.3010)
-0.2634 ANT.
r=0.5452

13.- (4/7) 8/38/3 (log 4/7)
8/3 log (0.5714)
8/3(-0.2430)
-0.6481 ANT.
r=0.2248

14.- (9/2) 7/8

7/8 (log 9/2)
7/8 log (4.5)
7/8 (0.6532)
0.5715 ANT.
r=3.7282

15.- (7/3) 4/74/7 (log 7/3)
4/7 log (2.33)
4/7 (0.3673)
0.2099 ANT.
r=1.6214

Logaritmos

Logaritmos

Propiedades de logaritmos

Propiedad 1    AxB
Log a + log b

Ejemplos:

A   B  3x5
Log 5+ log 3
.6989+.4771
1.1760 ANT.
r= 14.996

(.7081) (3.14)
Log.7081+log3.14
-0.1499+.4969
.3470
r= 2.2223

Propiedad 2
A /B  log a-log b
20/5
1.3010-0.6989
0.6021 ANT.
r= 4

0.1523/0.4785
Log 0.1523-log 0.4785
-8173- (-0.3201)
-8173+0.3201
-0.4972 ANT.
r= 0.3182

35/4.173

Log35-log4.173
1.5440-0.6204
0.9236 ANT.
r=8.386

Ejercicios

Propiedad 1

1.-A b    8x2
log 8 + log 2
.9030+.3010
1.204 ANT.
r=16

2.-A b    
2x3
log 2 + log 3
.3010+0.4771
0.7781 ANT.
r=5.891035415

3.-A b    
 9x5
log 9 + log 5
0.542+0.6989
1.6531 ANT.
r=44.9883

4.-A b 
    8x4
log 8 + log 4
0.9030+0.6020
1.5050ANT.
r=31.9889

5.-A b  
   7x3
log 7 + log 3
0.8450+0.4771
1.3221 ANT.
r=20.99423238

6.-A b 
   2x3
log 2 + log 3
0.3010+04771
0.7781 ANT.
r=4.668049099

7.-A b  
   4x2
log 4 + log 2
0.6020+0.3010
0.9030 ANT.
r=7.9983

8.-A b   
  3x2
log 3 + log 2
0.4771+.3010
0.7781 ANT.
r=5.999

9.-A b
     6x4
log 6 + log 4
0.7781+0.6020
1.3801 ANT.
r=23.9938

10.-A b      
 8x7
log 8 + log 7
0.9030+0.8450
1.7480 ANT.
r=55.9757

Con decimales

11.- A b  
 1.12x3.14
log1.12+log3.14
0.0492+0.4969
0.5461  ANT.
r= 1.92031

12.- A b  
    3.4x8.9
log3.4+log8.9
0.5314+0.9493
1.4807 ANT.
r=30.2428

13.- A b
  .1416x 1.1213
log.1416+log1.1213
-0.848+0.497
-0.351 ANT.
r=30.2428

14.- A b
1.1612x2.1012
log1.1612+log2.1012
0.0649+0.3224
0.3873ANT.
r=2.100873

15.- A b
2.3x1.2
log2.3xlog1.2
0.3617+0.07918
0.44088 ANT.
r=2.7598

16.- A b
0.1218x1.1417
log0.1218xlog1.1417
-0.9143+0.0575
-0.8567 ANT.
r=0.1390

17.- A b
0.9412x1.1711=1.1020
log.9412+log1.1711
-0.0263+0.0685
0.0422 ANT
r=1.1020

18.- A b
8.942x1.213
log8.942+log1.213
0.9514+0.0838
0.0422 ANT
r=10.8442

19.- A b
0.2214x1.1703
log.2214xlog1.1703
-0.6548+0.0682
-0.5866 ANT.
r=0.2590

20.- A b
1.5x2.3
log 1.5+log2.3
0.1760+0.3617
0.5377 ANT.
r=3.4490

Logaritmos

Propiedad 2

A/B
Log A -log B

1.- 22/17=1.2941log 22- log 17
1.3424-1.2304
-0.1119 ANT.
r=0.7728

2.- 4/3Log 4-log3
0.6020-0.4771
0.1249 ANT.
r=1.33

3.- 12/4Log 12-log 4
1.079-.6020
0.477 ANT.
r=2.999

4.- 42/8 =5.25log 42-log8
1.6232-0.9030
0.7202
r=5.2504

5.- 8/2 =4Log8-log2
0.9030-0.3010
0.602 ANT.
r=2.407

6.-9/8 =1.125log 9 – log 8
0.9542-0.9030
0.0512 ANT.
r=1.125

7.- 18/8 =2.25log 18-log8
1.2550.9030
0.352 ANT.
r=2.2490

8.- 20/4 =5log 20 – log 4
1.3010-0.6020
0.699ANT.
r=5

 9.- 42/7 = 6log 42-log 7
1.6232-0.8450
0.7782 ANT.
r=6

10.- 91/9=10.11log 91-log 9
1.9590-0.9542
1.0048 ANT.
r=10.11

Punto decimal

1.- 1.1213/.1412 = 7.9412log 1.1213-log.1412
0.0497-(-0.8501)
0.0497+0.8501
0.89981 ANT.
r=7.9398

2.- 3.1416/2.1811= 1.4403log 3.1416-log 2.1811
0.4971-0.3386
0.1585 ANT.
r=1.4404

3.- 8.1223/7.1204=1.1407log 8.1223-log 71204
0.9096-0.8525
0.0571 ANT.
r=1.1405

4.- 9.8312/1.2124 = 8.10887log 9.8312-log 1.2124
0.9926-0.0836
0.909 ANT.
r=8.108

5.- 14.1215/7.8523 =1.7983log 14.1215-log 7.8523
1.1498-0.8949
0.2549
r=1.7984

6.- 24.7784/12.1113 = 2.0458log 24.7784-log 12.1113
1.3940-1.0831
0.3109 ANT.
r=2.0458

7.- 30.8407/7.1218 = 4.33log 30.8407-log 7.1218
1.4891-0.8525
0.6366 ANT.
r=4.33

8.- 40.3238/11.15040=3.6163log 40.3238-log11.1504
1.6055-1.0472
0.5583 ANT.
r=3.6165

9.- 32.12/15.11 = 2.125744log 32.12-log15.11
1.5067-1.1792
0.3275 ANT.
r=2.1256

10.- 35.1817/8.1112 =4.3374log 35.1817-log 8.1112
1.5463-0.9090
0.6373 ANT.
r=4.3381

Enteros y punto decimal

1.- 44/1.5= 29.33log 44-log1.5
1.6434-0.1760
1.4674
r=29.33

2.- 55/8.9 =6.1797log 55-log8.9
1.74-0.94
0.8 ANT.
r=6.30

3.- 48/3.12 =15.3846log 48- log 3.12
1.6812-0.4941
1.1871 ANT.
r=15.3850

4.- 453/12.3=36.8292log 453-log12.3
2.6560-1.0899
1.5661 ANT.
r=36.8213

5.- 85/3.175 = 26.7716

Log 85-log3.175
1.9294-0.5017
1.4277 ANT.
r=26.7731

6.-49/3.121= 15.7000log49-log3.121
1.6901-0.4942
1.1959 ANT.
r=15.7000

7.- 98/8.123 = 12.0645log 98-log8.123
1.9912-0.9097
1.0815
r=12.0642

8.- 32/1.25=25.60log32-log1.25
1.5051-0.0969
r=25.59

9.-53/9.82= 5.3971log 53 - log 9.82
1.7242-0.9921
0.7321
r=5.3963

10.-47/3.141 =14.9633log47-log3.141
1.6720-0.4970
1.175 ANT.r=14.9623