Number expressed

Logarithm

Number

exponentially

(log)

10000

104

4

1000

103

3

100

102

2

10

101

1

1

100

0

0.1

10-1

-1

0.001

10-3

-3

0.0001

10-4

-4

It is easily seen that the exponent (power) to which the number ten has been

raised is the same as the logarithm.

A logarithm is composed of two parts.

a. The characteristic is the portion of the logarithm that lies to the left of the

decimal point. It is a whole number that may be negative or positive, depending upon

the original number.

b. The mantissa is the portion of the logarithm that lies to the right of the decimal

point. The mantissa is a decimal fraction of one (1) and it is always positive.

c. For example, the logarithm of 20 is equal to 1.3010, where the number one is

the characteristic and the number .3010 is the mantissa.

In order to find the logarithm of a number, the characteristic must first be

determined. The characteristic is always determined by inspection of the original

number or by applying a simple rule.

a. **By Inspection.**

(1) If we take the number 20, we see that it lies between 10 and 100, which

have logarithms of one and two, respectively. Therefore, the logarithm of the number

20 must be between one and two. The logarithm of 20 is 1.3010 and hence the

characteristic (remembering that the characteristic is the number to the left of the

decimal point) of the logarithm is one.

MD0837

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