domingo, 27 de marzo de 2011

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.- 12/4
Log 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