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.

• Exponential : exp. The function exp calculates online the exponential of a number.
• Logarithmic expansion : expand_log. The calculator makes it possible to obtain the logarithmic expansion of an expression.
• Napierian logarithm : ln. The ln calculator allows to calculate online the natural logarithm of a number.
• Logarithm : log. The log function calculates the logarithm of a number online.