b. Example 2. Find the logarithm of 0.000412.
0.000412 = 4.12 X 10-4
log (4.12 X 10-4) =
log 4.12 + log 10-4 =
0.6149 + (-4) =
4.6149 or equivalently, with a calculator, -3.3851
1-38. DETERMINATION OF ANTILOGARITHMS
The antilogarithm (antilog) is the number corresponding to a logarithm. For
example, the antilogarithm of three is the number whose logarithm equals three. The
number whose logarithm equals three is 1000; thus, the antilogarithm of three is 1000.
a. Mantissa. The mantissa of the logarithm can be found in the table of
"common" logarithms, and the three digits corresponding to the mantissa is written
down. In the event that the exact mantissa value is not in the table, find the closest
mantissa in the columns without exceeding the value of the mantissa being worked with.
Remember the mantissa is the number to the right of the decimal point.
b. Characteristic. The characteristic of the logarithm determines where the
decimal point will be placed in the number corresponding to the mantissa when
determining the antilogarithm.