# logarithm

The log function calculates the logarithm of a number online.
log(1), returns 0

### Log, online calculus

#### Summary :

The log function calculates the logarithm of a number online.

# Logarithm function

The logarithm function is defined for any number belonging to the interval ]0,+oo[, it notes log.

The logarithm calculator allows calculation of this type of logarithm online.

## Calculation of the logarithm

For the calculation of logarithm of a number, just enter the number and apply the function log. Thus, for calculating logarithm of the number 1, you must enter log(1) or directly 1, if the button log already appears, the result 0 is returned.

## Derivative of logarithm

The derivative of the logarithm is equal to 1/(x*ln(10)).

## Antiderivative of logarithm

The antiderivative of the logarithm is equal to (x*ln(x)-x)/ln(10).

## Limits of logarithm

The limits of the logarithm exist at 0 and +oo:
• The logarithm function has a limit in 0 which is -oo.
• lim_(x->0)log(x)=-oo
• The logarithm function has a limit in +oo which is +oo.
• lim_(x->+oo)log(x)=+oo

#### Syntax :

log(x), x is a number.

#### Examples :

log(1), returns 0

#### Derivative logarithm :

To differentiate function logarithm online, it is possible to use the derivative calculator which allows the calculation of the derivative of the logarithm function

The derivative of log(x) is derivative(log(x))=1/(ln(10)*x)

#### Antiderivative logarithm :

Antiderivative calculator allows to calculate an antiderivative of logarithm function.

An antiderivative of log(x) is antiderivative(log(x))=(x*log(x)-x)/ln(10)

#### Limit logarithm :

The limit calculator allows the calculation of limits of the logarithm function.

The limit of log(x) is limit(log(x))

#### Graphic logarithm :

The graphing calculator is able to plot logarithm function in its definition interval.