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.
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:
e \approx 2.71828182845904523536028747135266249775724709
(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, since d/dx ln(x) = 1/x, ln(x) shows up constantly in calculus.
Natural Logarithm Formula
The formula for the natural logarithm is:
log_{e}(x)=yWhere:
- 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:
ln(x), log(x), Log(x)
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:
\log_{e}(100)\ or\ e^y=100\\y\approx4.60517019In 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.
