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.

Want another tool? Try another logarithm calculator or the generic logarithm tool:

## Natural Logarithm Calculator

**Table of Contents**show ▼

## 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.*