Napierian logarithm : How to use it?
The ln calculator allows to calculate online the natural logarithm of a number.
Syntax :
ln(x), x is a number.
Examples :
ln(`1`), returns 0
Derivative napierian logarithm :
To differentiate function napierian logarithm online, it is possible to use the derivative calculator which allows the calculation of the derivative of the napierian logarithm function
The derivative of ln(x) is derivative(`ln(x)`)=`1/(x)`
Antiderivative napierian logarithm :
Antiderivative calculator allows to calculate an antiderivative of napierian logarithm function.
An antiderivative of ln(x) is antiderivative(`ln(x)`)=`x*ln(x)-x`
Limit napierian logarithm :
The limit calculator allows the calculation of limits of the napierian logarithm function.
The limit of ln(x) is limit(`ln(x)`)
Inverse function napierian logarithm :
The inverse function of napierian logarithm is the exponential function noted exp.
Graphic napierian logarithm :The graphing calculator is able to plot napierian logarithm function in its definition interval.
Napierian logarithm function
The napierian logarithm function is defined for any number belonging to the interval ]0,`+oo`[, it notes ln. The napierian logarithm is also called natural logarithm.
The logarithm calculator allows calculation of this type of logarithm online.
Calculation of the napierian logarithm
For the calculation of napierian logarithm of a number, just enter the number and apply the function ln. Thus, for calculating napierian logarithm of the number 1, you must enter ln(`1`) or directly 1, if the button ln already appears, the result 0 is returned.
Derivative of napierian logarithm
The derivative of the napierian logarithm is equal to `1/x`.
Calculate chain rule of derivatives with napierian logarithm
If u is a differentiable function, the chain rule of derivatives with the napierian logarithm function and the function u is calculated using the following formula : (ln(u(x))'=`(u'(x))/(u(x))`.
The derivative calculator can perform this type of calculation as this example shows calculating the derivative of `ln(4x+3)`.
Antiderivative of napierian logarithm
The antiderivative of the napierian logarithm is equal to `x*ln(x)-x`.
Limits of napierian logarithm
-
The limits of the napierian logarithm exist at `0` and `+oo`:
- The napierian logarithm function has a limit in `0` which is `-oo`.
- The napierian logarithm function has a limit in `+oo` which is `+oo`.
- `lim_(x->0)ln(x)=-oo`
- `lim_(x->+oo)ln(x)=+oo`
Propriété du logarithme népérien
The natural logarithm of the product of two positive numbers is equal to the sum of the natural logarithm of these two numbers. We can thus deduce the following properties:
- `ln(a*b)=ln(a)+ln(b)`
- `ln(a/b)=ln(a)-ln(b)`
- `ln(a^m)=m*ln(a)`
The calculator makes it possible to use these properties to calculate logarithmic expansions.
- 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.