Original

Number

Characteristic

Mantissa

Logarithm

_

0.2

-1

3010

1.3010

20

1

3010

1.3010

200

2

3010

2.3010

2000

3

3010

3.3010

20000

4

3010

4.3010

_

0.030

-2

4771

2.4771

412

2

6149

2.6149

5490

3

7396

3.7396

The determination of the logarithm becomes quite simple when the original

number is written in scientific notation; i.e., as an exponential expression. This form of

expressing the original number also should help you understand the meaning of the

characteristic and the mantissa.

a. **Example 1. **Find the logarithm of the number 4120.

Solution. First write 4120 in exponential form.

4120 becomes 4.12 X 103

Take the logarithm of the exponential expression.

log (4.12 X 103)

When determining the logarithm of two numbers being multiplied together (4.12 X 103),

the logarithm of each number is determined and the logarithms are then added.

log (4.12 X 103) = log 4.12 + the log 103

The logarithm of 4.12 is 0.6149 (mantissa) and the logarithm of 103 is three

(characteristic). Thus, the logarithm of 4120 = 0.6149 + 3 or 3.6149.

MD0837

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