# Why ln 1 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

The Logarithm calculatorenables 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.

### Derivation from the natural logarithm

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

### Derivation from a function that is composed with a natural logarithm

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.

### Antiderivative of the natural logarithm

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

### 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

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:

• `ln (a * b) = ln (a) + ln (b)`
• `ln (a / b) = ln (a) -ln (b)`
• `ln (a ^ m) = m * ln (a)`

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)