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Page Title:
Logarithms of Numbers Expressed as Exponentials |
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  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
1-37. LOGARITHMS OF NUMBERS EXPRESSED AS EXPONENTIALS
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
1-34
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