Natural Logarithm Calculator

Natural logarithm calculator. ln(x) calculator.

The natural logarithm of x is:

ln x = log_e x = y

Enter the input number x and press the  =  button:

ln
Result:

Natural Logarithm Calculator

The Natural Log Calculator is used to calculate the natural logarithm of a number x, which is generally written as ln(x) or log_e(x).The natural log calculator determines the logarithm to the base of a famous mathematical constant, e, an irrational number with an approximate value of e = 2.71828. But, what is the natural logarithm, ln x, of a given number x? This is the power the number e has to be raised to in order to result in a given number x.

Natural logarithm definition

The natural logarithm is the logarithm to the base e (Euler's number, approximately equal to 2.718281828). It is generally written as ln(x), log_e(x) or sometimes, if the base of e is implicit, as simply log(x). It is often used in mathematical analysis, physics, chemistry, statistics, economics, and some engineering fields.

The natural logarithm of x is the base e logarithm of x:

ln x = log_e x = y

ln(x) = y

x: is real number, x>0

Natural logarithm symbol is ln

ln(x) = y

ln(x) is equivalent of log_e(x)

How to use the natural logarithm calculator

Like all other logarithms, the natural logarithm of x returns the power, or exponent, to which a given base e must be raised to yield back the number x. It is easier to understand this notion when the base is an integer, for example 2 or 3:

log₂ 16 = 4 since 2⁴ = 16

log₃ 81 = 4 since 3⁴ = 81.

In the case of the natural logarithm, this is somewhat less intuitive, because it's base, e, is not an integer. But, since the value of e is between values of 2 and 3, we understand that e⁴ has to be somewhere between 2⁴ = 16 and 3⁴ = 81.

It turns out that e⁴ = 54.498. This equality can be stated in terms of the natural logarithm in the following way, which you can check by using the ln calculator:

ln 54.498 = 4

Here are some examples of Natural Logarithm Examples

ln(2) = log_e(2) = 0.6931

ln(3) = log_e(3) = 1.0986

ln(4) = log_e(4) = 1.3862

ln(5) = log_e(5) = 1.609

ln(6) = log_e(6) = 1.7917

ln(10) = log_e(10) = 2.3025

Check out the correctness of the above results by using our natural log calculator and the exponent calculator.