# Logarithms

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A mathematical system of representing the relation between a number which is split into number of multiplying factors on the basis of another number and the total number of multiplying factors is called the logarithm.

In earlier days, there was no calculating devices like calculators, computers and etc. and it was not easy to do some mathematical operations like multiplication, division and etc. with larger numbers and smaller numbers but logarithmic system made them easier. Now, there is no much importance because of the availability of the very advanced calculating devices. However, it is still used when the calculating devices fail.

Exponentiation is the required knowledge to understand and start learning logarithms in mathematics.

### Introduction

Logarithm is an inverse operation to the exponentiation. In exponentiation, a number is multiplied to itself number of times and the product of them is denoted in exponential notation.

For example, number $2$ is multiplied by itself $5$ times and the product of them is $32$.

$2 \times 2 \times 2 \times 2 \times 2 = 32$

It is expressed simply in exponentiation in exponential notation.

$2^5 = 32$

The same operation is done in logarithms inversely and it is written in mathematics as follows by using log symbol.

$\log_{2} 32 = 5$

### Logarithmic Identities

There are three basic and four advanced properties in logarithms and all of them are expressed in algebraic form to use them as formulas in theorems and problems. Here is the list of fundamental laws with proofs for beginners.