using log tables
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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
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using log tables
- 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
- 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)