using log tables

HOW TO USE LOG TABLES FOR ARITHMETIC CALCULATIONS

1. USING LOG TABLES FOR CALCULATION

2. All logarithms here are to the base 10 log(ab) = log a + log b log (   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  

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

4. log ( 0.02368). Ch =   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

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

6. 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

7. antilog (2.7682)=586.4

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

9. = 4.065 y = antilog 4.065 = 11610

10. Question 2 E valuate   Let y =   log y =log(23.87)-log (486.32) =1.3781- 2.6869 =   -2.6869  

11.   = 0.04911 Question 3   Let y =  

12. log y =        

13.       =.9016