Calculate the natural log of any number. Enter the number which you want to calculate the natural log of and this calculator will evaluate ln(x).
Natural Log Formula
The natural logarithm is a specific log that has a base of a mathematical constant. This const is e. (e) is an irrational number that roughly equals 2.718281828459. Instead of using the standard nomenclature of logarithms, which typically look like log(base,X), the natural log used the symbol ln(x).
This mathematical concept originally appeared in 1949 when studying the nature of hyperbola. Specifically the hyperbola xy=1. It was defined as the area of the hyperbolic sectors of this graph xy=1. Their solution was to name the hyperbolic logarithm, which was later renamed the natural log.
As mentioned above, e is equal to approximately 2.718281828459, and this calculator uses that as a base for the log. In reality, e is equal to a summation of a series of infinite values. As a result, the ln can only be approximated, not found exactly.
The more powerful the computer, the more accurate it can estimate e through more and more summations. With that said, for most cases, the number above is sufficient as it yields an accuracy of greater than 99.99%.
What is natural log used for?
So what can this calculator be used for? Well, first you need to understand a little more about the natural log to be able to use it properly. We’ve gone into some detail above, but let’s dig a little deeper.
Ln(x) is equal to the inverse of e^x. Log for that matter if the inverse of base ^x. Intuitively. this can be explained as the time it takes to reach a certain level of growth, which is one use for this.
This is where we will end. The natural log is all about time and growth.
FAQ
What is the significance of the base ‘e’ in natural logarithms?
The base ‘e’ is a mathematical constant approximately equal to 2.718281828459, known for its unique properties in calculus, especially in the context of growth and decay processes.
How is the natural log different from other logarithmic functions?
Unlike other logarithmic functions that can have any positive number as their base, the natural log specifically uses the base ‘e’. This gives it unique applications in mathematics, particularly in calculus and differential equations.
Can the natural log be used in practical applications?
Yes, natural logs are used in a wide range of practical applications including compound interest calculations, growth models, and in various fields of science and engineering to model natural phenomena.
Why can’t the value of ‘e’ be determined exactly?
The number ‘e’ is an irrational number, meaning it cannot be expressed as a simple fraction and its decimal representation goes on forever without repeating. It is defined as the limit of (1 + 1/n)^n as n approaches infinity, thus making its exact value impossible to pinpoint but can be approximated closely for practical use.
