1. The document provides calculations using natural and base-10 logarithms. It includes taking logarithms of multiplication, division, roots, and solving logarithmic equations for variable x. 2. The calculations involve taking logarithms of various numbers, adding and subtracting logarithms, and setting logarithmic equations equal to solve for x. 3. The goal is to practice various logarithmic calculations and operations like finding logarithms, adding and subtracting them, and solving equations involving logarithms.

1. 1. Realizar los siguientes cálculos mediante logaritmos
naturales y de base 10:
a) y = 2345*3487 R: 8.177.015,00
𝑙𝑜𝑔𝑦 = 𝑙𝑜𝑔2345 + 𝑙𝑜𝑔3487
𝑙𝑜𝑔𝑦 = 3.370142847 + 3.542451947
𝑙𝑜𝑔𝑦 = 6.912594794
𝑦 = 106.912594794
𝒚 = 𝟖𝟏𝟕𝟕𝟎𝟏𝟒. 𝟗𝟗
b) y = 1256*3454.23 R: 4.338.512,88
𝑙𝑜𝑔𝑦 = 𝑙𝑜𝑔1256 + 𝑙𝑜𝑔3454.23
𝑙𝑜𝑔𝑦 = 3.0990 + 3.5384
𝑙𝑜𝑔𝑦 = 6.6373
𝑦 = 106.6373
𝒚 = 𝟒𝟑𝟑𝟖𝟓𝟏𝟐.𝟖𝟖
c) y = 5463/345 R: 15,83
𝑙𝑜𝑔𝑦 = 𝑙𝑜𝑔5463 − 𝑙𝑜𝑔345
𝑙𝑜𝑔𝑦 = 3.7374 − 2.5378
𝑙𝑜𝑔𝑦 = 1.1996
𝑦 = 101.1996
𝒚 = 𝟏𝟓. 𝟖𝟑
2. Realizar los siguientes cálculos mediante logaritmos
naturales y de base 10:
a) 𝒚 = 𝟏𝟓. 𝟒𝟓 𝟕R: 210.135.479,98
𝑙𝑜𝑔𝑦 = 𝑙𝑜𝑔15.457
𝑙𝑜𝑔𝑦 = 7𝑙𝑜𝑔15.45
𝑙𝑜𝑔𝑦 = 7(1.1889)
𝑙𝑜𝑔𝑦 = 8.3225
𝑦 = 108.3225
𝒚 = 𝟐𝟏𝟎𝟏𝟑𝟓𝟒𝟖𝟎. 𝟎𝟎
b) 𝒚 = 𝟓𝟏. 𝟏 𝟓.𝟐
𝑙𝑜𝑔𝑦 = 𝑙𝑜𝑔51.15.2
𝑙𝑜𝑔𝑦 = 5.2𝑙𝑜𝑔51.1
𝑙𝑜𝑔𝑦 = 5.2(1.7084209)
𝑙𝑜𝑔𝑦 = 8.8837
𝑦 = 108.8837

2. 𝒚 = 𝟕𝟔𝟓𝟐𝟐𝟒𝟏𝟕𝟑. 𝟎𝟐
c) 𝒚 = √ 𝟒𝟓𝟔𝟑
R: 7,697
𝑙𝑜𝑔𝑦 = 𝑙𝑜𝑔4561/3
𝑙𝑜𝑔𝑦 =
1
3
𝑙𝑜𝑔456
𝑙𝑜𝑔𝑦 =
1
3
(2.6590)
𝑙𝑜𝑔𝑦 = 0.8863
𝑦 = 100.8863
𝒚 = 𝟕. 𝟔𝟗𝟕
3. Realizar los siguientes cálculos mediante logaritmos
naturales y de base 10:
a) y = 453*213/670 R: 144,01
𝑙𝑜𝑔𝑦 = (𝑙𝑜𝑔453 + 𝑙𝑜𝑔213) − 𝑙𝑜𝑔670
𝑙𝑜𝑔𝑦 = 2.6561 + 3.3284 − 2.8261
𝑙𝑜𝑔𝑦 = 2.1584
𝑦 = 102.1584
𝒚 = 𝟏𝟒𝟒. 𝟎𝟏
b) y = (2300/3454)*(1200/45) R: 17,76
𝑙𝑜𝑔𝑦 = (𝑙𝑜𝑔2300 − 𝑙𝑜𝑔3454) + (𝑙𝑜𝑔1200 −
𝑙𝑜𝑔45)
𝑙𝑜𝑔𝑦 = (−0.1766 + 1.4260)
𝑙𝑜𝑔𝑦 = 1.2494
𝑦 = 101.2494
𝒚 = 𝟏𝟕. 𝟕𝟔
c) y = 0.1231/(231*0.112) R: 0,004758
𝑙𝑜𝑔𝑦 = 𝑙𝑜𝑔0.1231 − (𝑙𝑜𝑔231 + 𝑙𝑜𝑔0.112)
𝑙𝑜𝑔𝑦 = −0.9097 − (2.3636 − 0.9508)
𝑙𝑜𝑔𝑦 = −2.3225
𝑦 = 10−2.3225
𝒚 = 𝟎. 𝟎𝟎𝟒𝟕𝟓𝟖
4. Realizar los siguientes cálculos mediante logaritmos
naturales y de base 10
a) 𝒚 = ( 𝟐𝟑. 𝟒 ∗ 𝟒𝟓. 𝟒) ∗ (𝟏. 𝟓𝟒𝟓 𝟕) R=22323.95
𝑙𝑜𝑔𝑦 = (𝑙𝑜𝑔23.4 + 𝑙𝑜𝑔45.4) + (𝑙𝑜𝑔1.5457)
𝑙𝑜𝑔𝑦 = (𝑙𝑜𝑔23.4 + 𝑙𝑜𝑔45.4) + (7𝑙𝑜𝑔1.545)
𝑙𝑜𝑔𝑦 = (1.3692 + 1.6571 + 1.3225)

3. 𝑙𝑜𝑔𝑦 = 4.3488
𝑦 = 104.3488
𝒚 = 𝟐𝟐𝟑𝟐𝟑. 𝟗𝟓
b) 𝒚 = √ 𝟒𝟓𝟔𝟑
/√ 𝟐𝟏𝟏𝟓
R=2.64
𝑦 = 4561/3/2111/5
𝑙𝑜𝑔𝑦 = 𝑙𝑜𝑔456
1
3 − 𝑙𝑜𝑔211
1
5
𝑙𝑜𝑔𝑦 =
1
3
𝑙𝑜𝑔456 −
1
5
𝑙𝑜𝑔211
𝑙𝑜𝑔𝑦 = 0.8863 − 0.4649
𝑙𝑜𝑔𝑦 = 0.4214
𝑦 = 100.4214
𝒚 = 𝟐. 𝟔𝟒
5. Despejar el valor de x
a)𝟑. 𝟒𝟓 𝒙 = 𝟒𝟓𝟔
𝑙𝑜𝑔3.45 𝑥 = 𝑙𝑜𝑔456
𝑥𝑙𝑜𝑔3.45 = 𝑙𝑜𝑔456
𝑥 =
𝑙𝑜𝑔456
𝑙𝑜𝑔3.45
𝒙 = 𝟒. 𝟗𝟒𝟑𝟗
b) 𝟒𝟓𝟔 𝒙 = 𝟏𝟐𝟎𝟎R: 1, 15803759
𝑙𝑜𝑔456 𝑥 = 𝑙𝑜𝑔1200
𝑥𝑙𝑜𝑔456 = 𝑙𝑜𝑔1200
𝑥 =
𝑙𝑜𝑔1200
𝑙𝑜𝑔456
𝒙 = 𝟏. 𝟏𝟓𝟖𝟎𝟑𝟕𝟓𝟗
c) 𝟓𝟒𝟎𝟎 = 𝟔𝟕𝟎 𝒙R: 1,32069886
𝑙𝑜𝑔5400 = 𝑙𝑜𝑔670 𝑥
𝑙𝑜𝑔5400 = 𝑥𝑙𝑜𝑔670
𝑥 =
𝑙𝑜𝑔5400
𝑙𝑜𝑔670
𝒙 = 𝟏. 𝟑𝟐𝟎𝟔𝟗𝟖𝟖𝟔
d) 𝟐𝟖𝟎 = 𝟑𝟒𝟎𝟎/(𝟔𝟕𝟎 𝒙) R: 0,38368443
𝒍𝒐𝒈𝟐𝟖𝟎 = 𝒍𝒐𝒈𝟑𝟒𝟎𝟎− 𝒍𝒐𝒈𝟔𝟕𝟎 𝒙
𝑙𝑜𝑔280 = 𝑙𝑜𝑔3400 − 𝑥𝑙𝑜𝑔670
𝑥 = (𝑙𝑜𝑔3400 − 𝑙𝑜𝑔280)/𝑙𝑜𝑔670
𝑥 = (3.531478917 − 2447158031)/2.826074803
𝒙 = 𝟎. 𝟑𝟖𝟑𝟔𝟖𝟒𝟑
6. Despejar el valor de x

4. a) √ 𝟒𝟕𝒙
= 𝟒𝟑𝟎𝟎 R: 0,46019331
47
1
𝑥 = 4300
𝑙𝑜𝑔47
1
𝑥 = 𝑙𝑜𝑔4300
1
𝑥
𝑙𝑜𝑔47 = 𝑙𝑜𝑔4300
𝑥 = 𝑙𝑜𝑔47/𝑙𝑜𝑔4300
𝒙 = 𝟎. 𝟒𝟔𝟎𝟏𝟗𝟑𝟑𝟏
b)𝟒𝟎𝟎𝟎 = √ 𝟐𝟏𝟗𝒙
4000 = 219
1
𝑥
𝑙𝑜𝑔4000 = 𝑙𝑜𝑔𝟐𝟏𝟗
𝟏
𝒙
𝑙𝑜𝑔4000 =
1
𝑥
𝑙𝑜𝑔219
𝑥 = 𝑙𝑜𝑔219/𝑙𝑜𝑔4000
𝟎. 𝟔𝟒𝟗𝟕𝟓𝟏𝟓𝟔
7. Despejar el valor de x
a) 𝟐. 𝟖𝟓 𝒙 = 𝟏𝟖𝟖. 𝟎𝟐𝟖𝟕 R: 5
𝑙𝑜𝑔2.85 𝑥 = 𝑙𝑜𝑔188.0287
𝑥𝑙𝑜𝑔2.85 = 𝑙𝑜𝑔188.0287
𝑥 = 𝑙𝑜𝑔188.0287/𝑙𝑜𝑔2.85
𝒙 = 𝟓
b)𝟒𝟑. 𝟖 𝒙 = 𝟖𝟒𝟎𝟐𝟕. 𝟔𝟕
𝑙𝑜𝑔43.8 𝑥 = 𝑙𝑜𝑔84027.67
𝑥𝑙𝑜𝑔43.8 = 𝑙𝑜𝑔84027.67
𝑥 = 𝑙𝑜𝑔84027.67/𝑙𝑜𝑔43.8
𝒙 = 𝟑
c) 𝟏𝟔𝟔𝟗𝟔𝟐.𝟓𝟑 = 𝟏𝟓𝟎 𝒙 R=2,4
𝑙𝑜𝑔166962.53 = 𝑙𝑜𝑔150 𝑥
𝑙𝑜𝑔166962.53 = 𝑥𝑙𝑜𝑔150
𝑥 = 𝑙𝑜𝑔166962.53/𝑙𝑜𝑔150
𝒙 = 𝟐. 𝟒
d) 𝟓𝟎𝟎 = 𝟐𝟓𝟎𝟎/(𝟏𝟒𝟎𝒙) R: 0,32568886
𝑙𝑜𝑔500 = 𝑙𝑜𝑔2500 − 𝑙𝑜𝑔140 𝑥
𝑙𝑜𝑔500 = 𝑙𝑜𝑔2500 − 𝑥𝑙𝑜𝑔140
𝑥𝑙𝑜𝑔140 = 𝑙𝑜𝑔2500 − 𝑙𝑜𝑔500
𝑥 = (𝑙𝑜𝑔2500 − 𝑙𝑜𝑔500)/𝑙𝑜𝑔140
𝒙 = 𝟎. 𝟑𝟐𝟓𝟔𝟖𝟖𝟖𝟔

5. 8. Si log 2 = 0.301030 y log 4 = 0.602060, determinar el
valor de los siguientes logaritmos
a) log 8 R: 0.903090
𝑥 = 4 ∗ 2
𝑥 = 𝑙𝑜𝑔4 + 𝑙𝑜𝑔2
𝑥 = 0.602060 + 0.301030
𝒙 = 𝟎. 𝟗𝟎𝟑𝟎𝟗𝟎
b) log 16 R: 1,204120
𝑥 = 4 ∗ 4
𝑥 = 𝑙𝑜𝑔4 + 𝑙𝑜𝑔4
𝑥 = 0.602060 + 0.602060
𝒙 = 𝟏. 𝟐𝟎𝟒𝟏𝟐𝟎
c) log√ 𝟏𝟔 R: 0,602060 16
𝑥 = 4
𝒙 = 𝟎. 𝟔𝟎𝟐𝟎𝟔𝟎