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The following basic concepts and definitions are given here as a need for the understanding of other engineering and Radio Frequency concepts to be dealing with in further sections.

The Logarithm, Definition:

The logarithm of of a given number N is the exponent X to which the base b has to be elevated to attain such number, the base can be any positive number different from 1. (Further and deeper explanations on logarithms can be found in numerous excellent mathematical books).

Logarithms are mathematically expressed as: Logb N= X

As can be seen the logarithm is an exponential function.

Base 10 or Briggs Logarithms

The logarithms of base 10 are the most common logarithms used in engineering, the mathematical expression for it is:

Log10 N= X

Example 1

Find the logarithm base 10 of number 1000

Log10 (1000)= X

From tables or by using a scientific calculator it can be find that such number is 3, because 10 elevated to the third power is 1000, the resolved mathematical expression then is:

Log10 (1000)= 3, this is a very simple and obvious example, lets try one no so obvious.

Example 2

Find the logarithm base 10 of number 38400

Log10 (38400)= X

From tables or by using a scientific calculator we find that such number is 4.58433, because 10 elevated to the 4.58433 power is 38400, the resolved mathematical expression then is:

Log10 (38400)= 4.58433

Natural Logarithms or Neper Logarithm

In a natural logarithm the base is the number e = 2.3026, then the natural logarithm of a number is the exponent to which the base e must raised to attain such number.

The natural, logarithms are mathematically expressed as:

Lne N=X or simple Ln N= X

Example

Which is the Ln of the number 100?

From tables or from a scientific calculator the Ln of 100 is = 4.605, in other words, this is the exponent to which the base e must be raised to attain the number 100.

The natural logarithm and the logarithm of base 10 are related by the following relationship:

Ln N = 2.3026 (Log10 N), The Ln of a number can be found by knowing the Log10 multiplied by 2.3026

The Antilogarithm.

Definition:

The antilogarithm of a number in a given base is the base was elevated to the exponent X to attain such number.

Example

Log10 N= X

The logarithm of 100 base 10 is 2

The antilogarithm mathematically is expressed as:

Antilog10 X = N

From tables or using a scientific calculator

The antilog10 2 = 100

The same procedure applies to any base.

The Logarithm