On this page is a natural logarithm calculator. Enter a number to take the natural logarithm (log base e), and we'll return the result.
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Natural Logarithm Calculator
What is the Natural Logarithm?
The natural logarithm is a logarithm which uses the base e. e is an irrational number known as Euler's number and approximately equal to:
(and it keeps going from there).
The natural logarithm doesn't feel very natural. However, e is a special number. Basically, the rate of change – or slope – of the equation 𝑦=𝑒^𝑥 is equal to y.
Relatedly, the logarithm ln(x) has the derivative dx/dy = 1/x – making it easy to move back and forth in calculus when using the natural logarithm.
Natural Logarithm Formula
The formula for the common logarithm is:
Where:
- e: the base of the equation, Euler's number (we raise e to the yth power to get x)
- x: the argument; the number we need e^y to equal
- y: the power or exponent we need to find
The natural logarithm is also written in a few other ways:
But be careful - log(x) and Log(x) more commonly refer to the common logarithm, or log base 10. In all of these forms the base e is assumed.
Natural Logarithm Example
For example, let's say you wanted to find the log base e of 100. Here's how it'd look:
In this case you need to raise e to the 4.605...th power to get 100.
Using the Natural Logarithm Calculator
Enter one number to get the natural logarithm: the argument x. Enter that to match a sentence form of "log base e of x" or "natural logarithm of x".
When finished, hit the button to Compute Natural Logarithm.
After this, try our other tools and calculators.
