# Exponentials and logarithms

Source: https://projectalevel.co.uk/maths/calculus/exponentials_and_logarithms

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**The Exponential function**
The exponential function is the function whose derivative is equal to its equation. In other words:

![](https://content.projectalevel.co.uk/img/maths/diff9.gif)

Because of this special property, the exponential function is very important in mathematics and crops up frequently.
Like most functions, the exponential has an inverse function, which is ln x (pronounced 'log x').

![](https://content.projectalevel.co.uk/img/maths/diff10.gif)

**The Natural Logarithm**
ln x is also known as the natural logarithm. The derivative of ln x is 1/x.
It therefore follows that the integral of 1/x is ln x + c .

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