Use of logarithmic tables
- 1. Mukesh N. Tekwani Ismail Yusuf College Of Arts, Science & Commerce Mumbai mukeshtekwani@outlook.com
- 2. Invented by John Napier – a Scottish mathematician. Developed in 16th century
- 3. Consider the following calculation 3.142 x 12.05 x (3.142)2 This calculation is quite complex without a calculator. One way is to do multiplication by manual way Second way => use calculator (NOT ALLOWED) Third way => use logarithmic tables
- 4. Consider the number 12. To find the logarithm of this number: Step 1: Find the characteristic Step 2: Find the mantissa
- 5. Step 1: Find characteristic Write the number by shifting the decimal point so that the number is between 1 and 10 Shift the decimal point and multiply by the appropriate power of 10. E.g. Consider the no. 12 12 = 12.0 = 1.2 x 101 (shift decimal point to left by 1 place) The power of 10 is the characteristic Therefore, characteristic is 1
- 6. Consider the number 235.7 This can be written as 2.357 x 102 Therefore, the decimal point had to be shifted to the left by 2 decimal places so that the number is between 1 and 10. 2 3 5 . 7 2 . 3 5 7 x 102
- 7. 78123 Characteristic ? 781.54 Characteristic? 3.142 Characteristic? 0.0067 Characteristic? 1538.2 Characteristic?
- 8. Mantissa is a pure fraction, and it is found from the log tables Example: Find log of 781.54 781.54 See in first column of log table Locate the digit 1 in the first row at top in middle portion of table Locate the digit 5 in top row of Mean Diff column
- 9. 1: Find characteristic (Characteristic = 2) 2: Find Mantissa In log table, see 78 in 1st column Locate the digit 1 in the first row at top The number at intersection is 8927 Locate digit 5 in Mean Difference column. The number is 3 8927 + 3 = 8930 So log(781.54) = 2.8930
- 10. Log( m x n) = Log M + log N
- 11. Find 851.9 x 11.82 Log (851.9) = 2. (9299 + 5) = 2.9304 Log (11.82) = 1. (0719 + 8) = 1. 0727 +________ 4. 0031 A/log(4.0031) = 1007 + 0 = 1007 Put decimal point after 1st digit: 1.007 x 104 So 851.9 x 11.82 = 1.007 x 104
- 12. Find 1234.9 x 9.8 Log (1234.9) = 3. (0899 + 17) = 3.0916 Log (9.8) = 0. (9912 + 0) = 0. 9912 +________ 4. 0828 A/log(4.0828) = 1210 Put decimal point after 1st digit: 1.210 x 104 So 1234.9 x 9.8 = 1.210 x 104
- 13. Find 1234.9 / 9.8 Log (1234.9) = 3. (0899 + 17) = 3.0916 Log (9.8) = 0. (9912 + 0) = 0. 9912 -________ 2.1004 A/log(2.1004) = 1259 + 1 = 1260 Put decimal point after 1st digit: 1.260 x 102
- 14. Find square root of 320 (320)1/2 = ½ log (320) = ½ x (2.5051) = 1.2525 A/Log(1.2525) 1786 + 2 = 1788 1.788 x101 = 17.88 Therefore square root of 320 is 17.88
- 15. 1/1.275 1.2 == first col 7 col 5 MD col 7874 - 33 = 0.7841