Question

What does $\ln$ stands for?

Answer 1

Logarithm function:

• A logarithm is defined as the inverse of exponents and can be used to calculate an unknown variable in the exponents.
• $\ln$ stands for natural logarithm. It is the logarithm value to the base $e$.
• A natural logarithm can be represented as $\ln \left(x\right)$ or ${\log }_e\left(x\right)$.
• $e$ is an irrational and transcendental number that is approximately equal to $2.71828182845$
• The exponential form of natural logarithm is $e^x=y$

Properties of Logarithm

1. Multiplication rule: $\mathbf{ln}\mathbf{\left(}\mathbf{mn}\mathbf{\right)}\mathbf{=}\mathbf{ln}\mathbf{\left(}\mathbf{m}\mathbf{\right)}\mathbf{+}\mathbf{ln}\mathbf{\left(}\mathbf{n}\mathbf{\right)},\mathbf{[}\mathbf{m}\mathbf{,}\mathbf{n}\mathbf{>}\mathbf{0}\mathbf{]}$
2. Quotient rule: $\mathbf{ln}\mathbf{\left(}\frac{\mathbf{m}}{\mathbf{n}}\mathbf{\right)}\mathbf{=}\mathbf{ln}\mathbf{\left(}\mathbf{m}\mathbf{\right)}\mathbf{-}\mathbf{ln}\mathbf{\left(}\mathbf{n}\mathbf{\right)},\mathbf{[}\mathbf{m}\mathbf{,}\mathbf{n}\mathbf{>}\mathbf{0}\mathbf{]}$
3. Reciprocal rule: $\mathbf{ln}\mathbf{\left(}\frac{\mathbf{1}}{\mathbf{x}}\mathbf{\right)}\mathbf{=}\mathbf{-}\mathbf{ln}\mathbf{\left(}\mathbf{x}\mathbf{\right)},\mathbf{x}\mathbf{>}\mathbf{0}$
4. Power rule: $\mathbf{ln}\mathbf{\left(}{\mathbf{x}}^{\mathbf{y}}\mathbf{\right)}\mathbf{=}\mathbf{y}\mathbf{·}\mathbf{ln}\mathbf{\left(}\mathbf{x}\mathbf{\right)},\mathbf{x}\mathbf{>}\mathbf{0}\mathbf{}\mathbf{and}\mathbf{}\mathbf{y}\mathbf{\in }\mathbf{R}$

Hence, meaning of $\mathbf{ln}$is explained.