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  1-32. EXAMPLES
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.
1-33. PARTS OF A 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.
1-34. DETERMINATION OF THE CHARACTERISTIC
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
1-30
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