Decimal logarithm . Also called the vulgar or Briggs logarithm system , it is known as the decimal logarithm system.
The set of logarithms of the numbers calculated on a given base is called the logarithm system. Due to its relationship with our numbering system, base 10 is the one that has found the greatest applications to logarithm calculation.
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- 1 Denotation
- 2 Calculation of decimal logarithms
- 3 Features
- 4 Mantissa
- 5 Sources
Due to their frequent use, decimal logarithms are denoted without writing the base, that is, instead of log 10 N we write log N and it is understood that the base is 10.
Decimal logarithm calculation
To calculate decimal logarithms, there are tables, and it is necessary to know that the logarithm of a number is another number that, in general, has an integer part and a decimal.
The integer part of a decimal logarithm depends only on the number of digits the number has as shown below.
Therefore log k = k
The integer part of a logarithm is called the characteristic If N is a number that has k integers, it must be: As you can see: The characteristic of the decimal logarithm of a number of k integers is k – 1 If 0 <N <1 and begins with k ceos including the zero before the comma we have: Then: The characteristic of the logarithm of a number that begins with k zeros is –k.
The decimal part of the logarithm is called the mantissa and does not depend on the position of the decimal point.
If N is any number of five whole numbers we can represent it in the following way:
N = a 1 to 2 to 3 to 4 to 5 and for example:
The numbers 1 to 2 to 3 to 4 to 5 and 1 to 2 to 3 , to 4 to 5 have the same sequence of digits, in the same order, and only the position of the comma changes. Their logarithms differ only by an integer, which in this case is 2, then, necessarily, their decimal parts (mantissas) have to be equal.