b. **Example 2. **Find the logarithm of 0.000412.

Solution.

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

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.

Examples.

Corresponding

Mantissa

Digits

0.8451

700

0.3010

200

0.2945

197

0.6981

499

0.9996

999

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.

MD0837

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