# The Logarithmic Function.

**The Logarithm.**

If “x” is a number and,

Then , “y” is known as the logarithm of “x” to the base “a”.

For example:

:-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:**

The function in which the relationbetween input(let x) and and output(let y)

is given by:

, where “a” is a constant,

is known as the logarithmic function.

when,

,

“y” is known as the logarithmic function of “x” to the base “a”. and denoted as:

**Relation between Exponential function and Logarithmic function:**

Exponential function and Logarithmic are inverse function of each other if they are on the same base.

For example:

:- When ,

“8″ is the Exponential function of “3″ and “3″ is the logarithmic function of “8″ to the base “2″.

**Note: **

**:- **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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