1. The document discusses using logarithm tables to calculate logarithms and antilogarithms. It provides examples of calculating the characteristic and mantissa of logarithms, as well as using the tables to find logarithms and antilogarithms. 2. Three sample calculation problems are presented: multiplying two numbers using logarithms, dividing two numbers using logarithms, and calculating a root of a number using logarithms. The steps to solve each using logarithm tables are shown. 3. Logarithm tables are used to look up values corresponding to parts of logarithms and antilogarithms in order to calculate the final value. Characteristics and mantissas are determined before using the tables to evaluate logarithms

1. USING LOG TABLES
FOR CALCULATION

4. All logarithms here are to the base 10
log(ab) = log a + log b
log (
𝑎
𝑏
) = log 𝑎 − log 𝑏
log (23.6827) has 2 parts the characteristic ie the part before the decimal point
and the mantissa ie the part after the decimal point
log 𝑎 𝑚 = 𝑚𝑙𝑜𝑔𝑎

5. log (23.6827) Characteristic = 1( no of digits before the decimal point -1)
log (236.82). Ch = 2
log (0.368). Ch = 1
log (2.368). Ch = 0

6. log ( 0.02368). Ch = 2
To calculate mantissa, we consider the first 4 significant digits
We look at 23 in the leftmost column ( it is actually 2.3)
Under column 6 it is 3729
In the same row look under column 8 in the extreme right
It is 15
Add 3729 + 15 = 3744

7. log(23.6827) = 1. 3744
log(0.2368) = 1. 3744
To calculate antilog (1.7682) in the antilog table look at .76 ander column 8

8. It is 5861
In the same row look under 2 in the extreme right . It is 3
5861+3 = 5864
Count the number of digits before 1.7682
Since it is 1, put the decimal point after 2 digits
Antilog (1.7682) = 58.64

9. antilog (2.7682)=586.4

12. Question 1
(23.87)(486.32)
Let y = 23.87(486.32)
log y = log 23.87 + log 486.32
=1.3781 + 2.6869

13. = 4.065
y = antilog 4.065
=11610

16. Question 2
Evaluate 23.87
486.32
Let y = 23.87
486.32
log y =log(23.87)-log (486.32)
=1.3781- 2.6869 = 2. 6912
1.3781
-2.6869
2. 6912

17. 𝑦 = 𝑎𝑛𝑡𝑖𝑙𝑜𝑔 2. 6912
= 0.04911
Question 3
(0.7365)
1
3
Let y = (0.7365)
1
3

18. log y =
1
3
log(0.7365)
=
1
3
(1. 8672)
=
2 + 3. 8672
3
=
2
3
+ 1. 2890

19. = .6666 + 1. 2890
=
1. 9550
=.9016
𝑦 = 𝑎𝑛𝑡𝑖𝑙𝑜𝑔(1. 9550)