What is Logarithm?

A process of calculating the total number of factors in a quantity when the quantity is split as a product of factors in another quantity, is called logarithm.

Introduction

A quantity can be written as factors to express the quantity as the product of two or more factors. In some cases, all factors can be same in the product. In this case, the quantity is completely expressed in terms of a factor. So, the quantity is divided as factors on the basis of another factor and the total number of factors is called the logarithm of a quantity on the basis of another quantity.

Concept

$8$ is a quantity and it is expressed in product form in terms of another quantity $2$.

$8 = 2 \times 2 \times 2$

$\implies 8 = \underbrace{2 \times 2 \times 2}_{3}$

The total number of factors is $3$ when the quantity $8$ is expressed as factors on the basis of another quantity $2$. This mathematical operation to find the total number of factors is called the logarithm.

Actually, the logarithm is an inverse operation of the exponentiation.

Representation

The relation between the quantity, base quantity and the total number of factors is expressed in mathematical form by logarithm.

1. The mathematical operation is denoted by logarithmic symbol $\log$
2. The quantity is written after the $\log$ symbol.
3. The base quantity is written as subscript of the log symbol to tell that the quantity is expressed as factors on the basis of this quantity.

Now, let’s express our example in logarithmic form.

$\log_{2}{8} = 3$

The mathematical equation expresses that the total number of factors is $3$ when the quantity $8$ is written as factors on the basis of the number $2$.

Examples

$(1).\,\,$ $\log_{2}{128}$

$(2).\,\,$ $\log_{0.3}{0.027}$

$(3).\,\,$ $\log_{\sqrt{3}}{9}$

List of the examples to learn how to find the logarithms of the quantities for practice and also to understand the process of finding the logarithm of any quantity on the basis of another quantity.