The Logarithmic Function.
If “x” is a number and,
Then , “y” is known as the logarithm of “x” to the base “a”.
:-The logarithm of 16 to the base 2 is 4 which can be shown as:
:-The logarithm of 8 to the base 2 is 3 which can be shown as:
The logarithmic Function:
is given by:
, where “a” is a constant,
is known as the logarithmic function.
“y” is known as the logarithmic function of “x” to the base “a”. and denoted as:
Relation between Exponential function and Logarithmic function:
:- When ,
“8″ is the Exponential function of “3″ and “3″ is the logarithmic function of “8″ to the base “2″.
:- Logarithmic function to the base 10 is known as common logarithm.
:- Logarithmic function to the base “e” is known as natural function where the value of “e” is given by:
and if the base of a logarithmic function is “e” then the base is usually omitted and written as:
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