**Definition** : A logarithm is the result of raising power of a number to which the logarithm is assigned. In other word we can say that logarithm is the power to which the given number is raised.

example : X= log_{10} 100=2 , is equal to log_{10}**10 ^{2 }**

so X= 2

The common form of logarithms are

1. 10 base logarithm or common logarithm

2. e base logarithm natural logarithm

3. 2 base logarithm or binary logarithm

**1. 10 base logarithm or common logarithm:**

logarithm with base 10 is called common logarithm . We usually known to this logarithm we sometime call it simply log that mean it has a base of 10.

for example log_{10} 100=2 , is equal to log_{10}**10 ^{2}**

that means we just need to raise the power of 10

log *x* to mean log_{10} *x*.

**Usefulness**: various engineering fields ,

logarithm tables, handheld calculators, spectroscopy

**2. e base logarithm natural natural logarithm**

A logarithm with base e is called e base logarithm or natural logarithm it is represented by **ln x**.

example : **For example:** loge4.

e is a constant whose value is approximately 2.178

**Usefulness**: mathematics, physics, chemistry,

statistics, economics, information theory, and engineering

**3. 2 base logarithm or binary logarithm**

We all might know about the decimal logarithm or 10 base log but do you also know about the **binary logarithm** (log_{2} *n*) logarithm of base 2.

Binary logarithm or base 2 logarithm is a logarithm where the power of 2 must be raised

for example:

here the power of 2 must be raised to obtain the value of x.

For example, the binary logarithm of 1 is 0, the binary logarithm of 2 is 1, the binary logarithm of 4 is 2 where 2 to the power 2 is 4, and the binary logarithm of 32 is 5.

**Usefulness**: computer science, information theory, music theory, photography