Resolver las siguientes ecuaciones:

Resolver las siguientes ecuaciones

1.- 7 (x+6) =5
(6) log 5 =log 7
log 0.6989=log .8450
log .8450/.6989=1.2090
1.2090/6=0.2015

2.-8 (2x-7) =3
(2x-7) log 3= log 8
log .4771=log .9030
.9030/.4771=1.8926
1.8926+7=8.8926
8.8926/2=4.4463

3.-4 (3x-5) =2
(3x-5) log 4=log 2
.6020=.3010
log 2/log 4
 .3010/.6020=.5+5=10.5/3
x=1.1666

4.-3 (½x-2)=.75
(½x-2)  log3=log .75
.4771=-0.1249
-0.1249/.4771=-0.2617
-0.2617+2=1.73831.7383/½=3.4766

5.- 9 (3/2x+½)=1.5
(3/2x+½) log 9=log 1.5
.9542=.1760
.1760/.9542=0.1844
0.1844-½=-0.3156
-0.3156/3/2=-0.1402

6.-.25 (3/2x)=.5
(3/2x) log .25=log.5
-.3010/-.6020=0.5
x=0.5/½=1

7.- 3.6 (1.7x)= .8
(1.7x) log 3.6=log .8
.5563=-0.0969
1.7x=-0.0969/.5563=-0.1741
-0.1741/1.7=-0.1024

8.-1.5 (3x) =2.5
(3x) log 1.5=log 2.5
0.1760=0.3979
3x= .3979/.1760=2.2607
2.2607/3=0.7535

9.-2.3 (5/2x) =5
(5/2) log 2.3=log 5
.3017=.6989
.6989/.3017=2.3165
x=2.3165/5/2=.9266

10.- 2 (7/3x) = 4/5
(7/3x) log 2 =log 4/5
.3010=-0.3219
-0.3219/7/3=-0.1379

11.- .8*=2.2
log .8=log 2.2
-0.0969=0.3424
x=0.3424/-0.0969
x=-3.5335

12.- .17*=.7
log .17=log .7
-0.7695=-0.1549
x=-0.1549/-0.7695=0.2012

13.- (3/2)* =3/2

14.- .56*=.97
log.56=log .97
-0.2518=0.0132
x=0.0132/-0.2518=-0.0524

15.-.8*=2.3
log .8=log 2.3
-0.0969=0.3617
x=0.3617/-0.0969=-3.7327

1.- 4 (3x+7-2x) =36
4 (1x+7) =36
log 4=log 36
.6020=1.5563
x= .15563/.6020=2.5852-=1.5852
1.5852/7=0.0323

2.- 3 (2/3x) =4
(2/3x) log 3=log 4
.4771=.6020
.6020/.4771=1.2617
1.2617/2/3=1.8925

3.-3.7 (2x-3+7x-1) =2
3.7 (1x+4)=4
log 3.7=log 2
.5682=.3010
x=.3010/.5682=.5297-1=-.4703
-.4703/4=-0.1175

4.-2.5 (1/2x) =.9
log 2.5=log .9
0.3979=-0.0457
-0.457/.3979=-0.1148
-0.1148/1/2=-0.2296

5.- 2 (7x-3-2x+6) =10
2 (5x+3) =10
log2=log 10
.3010=1
x=1/.3010=3.3222-3=0.3222
0.3222/5=0.01288

6.-3.2 (7x-3) =6
log 3.2=log6
.5051=.7781
.7781/.5051=1.5404+3=4.5404
4.5404/7=.6486

7.-5.7 (2/3x-7) =0.67
log 5.7=log 0.67
.7558=-0.1739
-0.1739/.7558=-0.2301+7=6.7698
0.7698÷2/3=10.1548

8.- 1.5 (6x-3) =4.7
(6x-3) log 1.5=log 4.7
.1760=.6720
.6720/.1760=3.818
3.818+3=6.8187
6.8187÷6=1.1364

9.- 4 (3x-7) =2.7
(3x-7) log 4=log 2.7
.6020=.4313
.4313/.6020=0.7164
.7164+7=7.7164
7.7164÷3=2.5721

10.- 2.3 (.5x-2) =.7
(.5x-2) log 2.3=log .7
.3617=-0.1549
-0.1549/.3617=-0.4282
-0.4282+2=1.5717
1.5717÷.5=3.1434

Resolución de ecuaciones

Resolución de ecuaciones

Ejemplos:

- 3(x) =8

 x log 3=log 8
x=log 8/log3
x=.9030/.4771=1.8863
3^1.8863=8

-5(2x-1)=2

(2x-1) log=log2
2x-1=log/log 5
2x-1=.3010/.6989
2x-1=.4306
2x=.4306+1
2x=1.4306/2
x=.7153
5^ (2x.7153-1)=5

1.- 5*=.17

x log 5=log .17
x=log.17/log5
x=-0.7695/.6989=-1.1010
5^-1.1010=.17

2.- .18*=3.16

x log .18=log 3.16
x= log 3.16/log .18
x=.4996/-0.7447=-0.6708
.18^-0.6708=3.16

3.-2.5 (2x) =4

(2x) log 2.5=log 4
(2x) log 4/log 2.5
(2x) .6020/.3979=1.5129
x=1.5129/2 =.7564
2.5^0.7564=4

4.-9*=8

x log 9=log 8
x=log 8/log 9
x=.9030/.9542=.9463
9^0.49463=8

5.-1.5 (5x) =5.5

(5x) log 1.5=log 5.5
(5x) log 5.5/1.5=3.6666
x=3.6666/5 0.7333
1.5^0.7333=5.5

6.- 3 (3x) =9

(3x) log 3 =log9
(3x) log 9/3
(3x).9542/.4771=2
x=3/2=1.5

7.- 3(2x-5)=5

2x+5 log=3=log5
2x+5= .6989/.4771
2x=1.4648-5
x=-3.5352/2
x=-1.7676

8.- 2.5 (2x-2)=10

(2x-2)  log 2.5=log 10
(2x-2)  1/.3979
2x=2.5131+2
x=4.5131/2
x=2.2565

9.-9 (3x-3) =6

(3x-3) log 9=log 6
3x-3= .7781/.9542
3x=.8154+3
x=3.8154/3
x=1.2718

10.- 3.5 (3x-1)=2.5

(3x-1) log 3.5=log 2.5
3x-1=.3979/.5440
x=1.7314/3
x=.5771

11.-3*=20

x= log 3= log 20
x=1.3010/.4771
x=2.7268

12.- 2 (3x) =.97

(3x) log 2= log .97
3x= -0.0438/3
x=-0.0146

13.- 3.5 (7x-1) =.87

(7x-1) log 3.5=log .87
7x-1=-0.0604/0.5440=-0.1110
x=0.889/7
x=.127

14.-.97 (2x) =.56

(2x) log .97=log .56
2x=-0.2518/-0.0132=19.0757
x=19.0757/2=9.5378

15.-2 (3x) =.89

(3x) log 2= log .89
3x=-0.0506/0.3010=-0.1681
x=-0.1681/3
x=0.0560

1.-2 (7x+1) =7

(7x+1) log 2 = log 7
7x+1= log 7/log 2
2.8073-1=1.8073
1.8073/7=.2581

2.-  2 (.7x) =.7

(.7x) log 2=log.7
(.7x) log .7/log 2
(.7x) -0.1549/.3010 =-0.5146
-0.5146/.7=-0.7351

3.-.2 (2x) =.5

(2x) log.2=log .5
(2x)= log .5/log.2
(2x) -0.3010/-0.6989=0.4306
0.4306/2=0.1076

4.- 3.5*=3.6

x log 3.5=log 3.6
x=log 3.6/log 3.5
x=.5563/.5440=1.0226

5.- 3 (2x) =10.5

2x log 3= log 10.5
2x= .4771/1.0211
2x=1.0211/2=2.1402
x=1.0701

6.- 9 (7x-10) =1

(7x-10) log1=log 9
(7x-10) log 9/log 1
.9542/0=0
0+10=10
10/7=1.42

7.-4.6*=35

x= log 4.6=log 35
x=.6627=1.5440
x=1.5440/.6627=2.32
x=2.32

8.- 5 (3x) =.58

(3x) log 5=log .58
3x= .6989=-0.2365x=-0.2365/.6989=-0.3384
-0.3384/3=-0.1128

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


(5x-1) log 2.3=log .9
x=.3617=-0.0457
-0457/.3617=-0.1265
-0.1265+1=.8735
.8735/5=.1747

10.-2*=27

x= log 2= log 27
.3010=1.4313
1.4313/.3010=4.7553
x=4.7553

Ejercicios del libro de Baldor

Logaritmos

Hallar el valor de las expresiones siguientes por medio de logaritmos:

1.- 532x0.184log 532+log0.184
2.7259+ (-0.7351)
2.7259-0.7351
1.9908 ANT.
r=97.9039

2.- 191.7x432log 191.7+log 432
2.2826+2.6354
4.9180 ANT.
r=82794.2163

3.-0.7x0.013x0.9log 0.7+log 0.013+log 0.9
-0.1549+ (-1.8860)+ (-0.0457)
-2.0866 ANT.
r=8.1921

4.-7.5x8.16x0.35x10037log 7.5+log 8.16+log 0.35 +log10, 037
0.8750+0.9116+ (-0.4559)+4.0016
5.3326 ANT.
r=215079.9862

5.- 3.2x4.3x7.8x103.4x00.19log 3.2+log 4.3+log 7.8+log 103.4+log 00.19
0.505+0.6334+0.8920+2.0145+ (-1.7212)
2.3237 ANT.
r=210.7172

6.-95.13÷7.23log 95.13-log 0.8591
1.1196 ANT.
r=13.1704

7.- 8.125÷0.9324log 8.125- log 0.9324
0.9098- (-0.0303)
0.9401 ANT.
r=8.7116

8.-7,653.95÷12.354log 7,653.95- log 12.354
4.8491-1.0918
3.7573 ANT.
r=5718.7353

9.- 0.72183/0.0095log 0.72183- log 0.0095
-0.1415-(-2.0222)
-0.1415+2.0222
1.8807 ANT.
r=75.9801

10.- 9,114/0.02log 9,114-log 0.02
3.9597-(-1.6989)
5.6586 ANT.
r=455617.0838

11.-
10 log 2
10 (0.3010)
3.01 ANT.
r=1023.2929

12.- 0.15³3 log 0.15
3(-0.8239)
-2.4717 ANT.
r=3.3752

13.-
4 log 18.65
4(1.2706)
5.0827 ANT.
r=120976.2171

14.- 00.84²2 log 00.84
2 (-0.0757)
-0.1514 ANT.
r=0.7056

15.-
6 log 7.2
6(0.8573)
5.1439  ANT.
r=139283.6054

16.-
3 ½
½ log 3
½ (0.4771)
0.2385 ANT.
r=1.7318

17.-
2 1/3
1/3 log 2
1/3 (.3010)
0.1003 ANT.
r=1.2597

18.-
5 ¼
¼ log 5
¼ (00.6989)
0.1747 ANT.
r=1.4952

19.-
1/5 log de 63
1/5 (1.7993)
0.3598 ANT.
r=2.2898

20.-
1/(7 log 815
1/7 (2.9111)
0.4158 ANT.
r=2.6049

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