Question

What is the difference between $\log$ and $\ln$?

Answer 1

Difference between $\log$ and $\ln$:

Logarithm or log:

The logarithm, also known as the logarithm of a number or a $\log$, is another way of expressing exponents.

It is a raised exponent $\left(\mathrm{x}\right)$ where $\mathrm{b}$ is the base, which yields the allowed number $\left(\mathrm{n}\right)$.

Logarithms can also be viewed as the opposite of exponentiation.

As a mathematical expression, $\mathrm{x}$ is the logarithm of $\mathrm{n}$ to the base $\mathrm{b}$, where ${\mathrm{b}}^{\mathrm{x}}=\mathrm{n}$:

$\Rightarrow {\log }_{\mathrm{b}}\mathrm{n}=\mathrm{x}$

Natural Logarithm or ln:

The logarithmic function to the base $\mathrm{e}$ is called the natural logarithmic function and it is denoted by ${\log }_e$.

$\Rightarrow \mathrm{f}\left(\mathrm{x}\right)={\log }_{\mathrm{e}}\mathrm{x}$

Difference between $\log$ and $\ln$:

1. $\log$ is denoted by common logarithm, where $\ln$ is denoted by natural logarithm.
2. The common $\log$ is represented as ${\log }_{10}\left(\mathrm{x}\right)$. The natural log is represented as ${\log }_{\mathrm{e}}\left(\mathrm{x}\right)$.
3. The distinction between $\log$ and $\ln$ is that $\log$ equals base $10$ while $\ln$ is equal to base $\mathrm{e}$.

Example:

$\log$ of base $2$ is represented by $={\log }_2$,

$\log$ of base $\mathrm{e}$ is represented by ${\log }_e=\ln$ (natural log).

Hence,

1. $\log$ is denoted by common logarithm, where $\ln$ is denoted by natural logarithm.
2. The common $\log$ is represented as ${\log }_{10}\left(\mathrm{x}\right)$. The natural log is represented as ${\log }_{\mathrm{e}}\left(\mathrm{x}\right)$.
3. The distinction between $\log$ and $\ln$ is that $\log$ equals base $10$ while $\ln$ is equal to base $\mathrm{e}$.