# What is the value of ln 0

## Natural logarithm

#### Summary :

With the function ln you can calculate the natural logarithm of a number online.

ln online#### Description :

The function **Natural logarithm** is defined for every number belonging to the interval] 0, `+ oo` [, it is with **ln**. The Napier logarithm is also called **Natural logarithm** designated.

- Calculation of the natural logarithm
- Derivation from the natural logarithm
- Derivation from a function that is composed with a natural logarithm
- Antiderivative of the natural logarithm
- Limit of the natural logarithm The limit values of the natural logarithm exist in `0` and` + oo` (plus infinity):
- The natural log function has a limit in 0 that is equal to `-oo`.
- The natural logarithm function has a limit in `+ oo` that is equal to` + oo`.
- Property of the natural logarithm
- `ln (a * b) = ln (a) + ln (b)`
- `ln (a / b) = ln (a) -ln (b)`
- `ln (a ^ m) = m * ln (a)`

The **Logarithm calculator**enables **calculation** this kind of **Logarithm online**

To the **Calculate the natural logarithm of a number**, just enter the number and apply the function **ln** at. For the **Calculation of the natural logarithm** the following number: 1 you must enter ln (`1`) or directly 1, if the button ln already appears, the result 0 is returned.

The derivative of the natural logarithm is equal to `1 / x`.

If u is a differentiable function, the **Derivation** a function that results from the ** Logarithmic function** and the function u **composed** , calculated according to the following formula: (ln (u (x)) '= `(u' (x)) / (u (x))`. The derivative calculator can carry out this type of calculation, as in this example the derivative calculation of ln (4x + 3) shown.

An antiderivative of the natural logarithm is equal to `x * ln (x) -x`, this result is achieved by integrating parts.

The natural logarithm of the product of two positive numbers is equal to the sum of the natural logarithm of these two numbers. Hence we can derive the following properties:

With the calculator, you can use these properties to calculate logarithmic expansion.

With the function ln you can calculate the natural logarithm of a number online.

#### Syntax:

ln (x), x is a number.#### Examples:

ln (`1`), returns 0#### Derivation natural logarithm:

To derive an on-line function Natural Logarithm, it is possible to use the Derivative Calculator which allows the calculation of the derivative of the Natural Log function Natural Logarithm

The **Derivative of ln (x)** is derivation calculator (`ln (x)`) = `1 / (x)`

#### Antiderivative natural logarithm:

The antiderivative calculator enables the calculation of an antiderivative of the natural logarithm function.

A **Antiderivative of ln (x)** is antiderivative (`ln (x)`) = `x * ln (x) -x`

#### Limit value natural logarithm:

The limit value calculator allows the calculation of the limit value of the natural logarithm function.

The **Limit of ln (x)** is limit value calculator (`ln (x)`)

#### Mutual function Natural logarithm:

The **Freeciprocal function of natural logarithm** is the function exponential function with exp.

#### Graphical representation of natural logarithm:

The online function plotter can draw the natural logarithm function over its domain.

Calculate online with ln (natural logarithm)

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