A logarithmic system which contains neper constant ($e$) as its base, is called natural logarithm.

John Napier, a Scottish mathematician who introduced logarithmic system firstly by an irrational mathematical constant $e$ (known as Napier constant).

He split the quantities as multiplying factors on the basis of his neper constant $e$. Thus a natural logarithmic table was introduced and it made calculations like multiplication and division easier.

John Napier developed this logarithmic system in natural mathematical approach. Therefore, it is generally called as natural logarithm and also often called as Napierâ€™s logarithms.

He defined the value of Napier constant as

$e \,=\, 2.718281828459\ldots$

Logarithm is simply denoted by $\log$ symbol and $e$ is used as subscript of log to express that $e$ is a base of the logarithm.

If $q$ is a quantity, then logarithm of $q$ to base $e$ is written in mathematical form as $\log_{e}{q}$. It is also written as $\ln{q}$ simply.

Therefore, $\log_{e}{q}$ and $\ln{q}$ both represent natural logarithm of quantity $q$ in mathematics.

Natural Logarithm and Exponentiation are inverse operations. So, it is very important to know the relation between them.

The total number of multiplying factors is $x$ when the quantity $q$ is divided as multiplying factors on the basis of another quantity $e$.

$\log_{e}{q} \,=\, x$ then $q \,=\, e^{\displaystyle x}$

Therefore, $\log_{e}{q} \,=\, x$ $\, \Leftrightarrow \,$ $q \,=\, e^{\displaystyle x}$

It can also be written as

$\ln{q} \,=\, x$ $\, \Leftrightarrow \,$ $q \,=\, e^{\displaystyle x}$

Latest Math Topics

May 21, 2023

May 16, 2023

May 10, 2023

May 03, 2023

Latest Math Problems

May 09, 2023

A best free mathematics education website that helps students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

A math help place with list of solved problems with answers and worksheets on every concept for your practice.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved