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Natural Logarithm Calculator

Written by:
PK

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

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, 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:

log_{e}(x)=y

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:

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\approx4.60517019

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.

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