# what is logarithm and its type?

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= log10 100=2 , is equal to  log10102

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 log10 100=2 , is equal to  log10102

that means we just need to raise the power of 10

log x to mean log10 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 (log2n) 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