# Logarithm

Learn logarithms easily from basics to advanced level for both beginners and advanced learners.

## Definition

A mathematical system that evaluates the total number of multiplicative factors on the basis of a number to obtain another number as their product is called the logarithm.

Any number can be expressed as number of multiplicative factors on the basis of another number.

The mathematical relation between a particular number and a number which considered as a parameter to express the number in its terms as multiplicative factors is known as logarithms.

Logarithm is symbolically denoted by $\log$ in mathematics to represent relation between them.

### Example

$32$ is a number and express it as multiplying factors on the basis of any number, for example $2$.

$32 = 2 \times 2 \times 2 \times 2 \times 2$
$\implies 32 = 2^{\displaystyle \, 5}$

Exponentiation is used to express the number $32$ in exponential notation and the form represents the relation between a number which considered as a parameter and the total number of its multiplicative factors.

Logarithm is used to represent the relation between a number and the number which considered as a base to get the number of its multiplicative factors.

$\log_{\displaystyle \, 2} 32 = 5$

#### Basics

Exponentiation is the required mathematical knowledge to start studying logarithms. If you already learned it, you are eligible to learn logarithms. So, learn the logarithmic basics firstly.

Learn how to express any number in exponential notation.

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