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54All ABout Slide RulesFind: The common logarithm of 21 (Log 21)Cursor to 21 on DMantissa = .322 at cursor on LLogarithm is 1.322 (Characteristic is 1, because 21 is between 10 (whosecharacteristic = 1) and 100 (whose characteristic = 2).Or we can say 10 to the 1.322 power = 21.Find: Log 2100Mantissa is still .322Characteristic is 3, because 2100 is between 1,000 (Characteristic = 3) and10,000 (Characteristic = 4).Logarithm is 3.32210 to the 3.322 power is 2100.Find: Log 2.1Mantissa is still .322Characteristic is now 0Logarithm is 0.322Find: Log 0.21To determine this logarithm, we must subtract 1 from Log 2.1. Subtracting1 from the logarithm is the same as moving the decimal point one place to theleft ... or the same as dividing by 10.Log 0.21 = 0.322 – 1.000 = – 0.678Find: Log 0.00021We now have a decimal point 4 places to the left of 2.1.Thus, we subtract 4 from Log 2.10.322 – 4.000 = – 3.678General procedure for determining logarithms of numbers less than 1:Determine the mantissa of the number as if it were between 1 and 10, usingyour L scale. Then subtract the characteristic for the number of places thedecimal point of your actual number is to the left of the whole single digitnumber.In the example above, the decimal point for 0.00021 is 4 places to the leftof the whole single digit number 2.1. So we subtract 4.You may note that the L scale is linear, from 0 to 10, with even divisionsjust like a ruler. In some 10” scale designs, it can actually be used as a ruler, butits purpose is to convert the logarithmic distances of the C and D scales to theirlinear equivalent, which we then read as the logarithm’s mantissa.We multiply and divide by adding and subtracting logarithmic distances onthe A, B, C, D, CI, DI, CIF, CF and DF scales. In fact, we could also add and