HOW TO USE LOG TABLES FOR ARITHMETIC CALCULATIONS

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)