• Revision:Exponentials and logarithms

TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Exponentials and Logarithms


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


\frac{\text{d}}{\text{d}x}e^x = e^x



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').


f(x) = e^x \Leftrightarrow f^{-1}(x) = ln x


The Natural Logarithm

\ln x is also known as the natural logarithm. The derivative of \ln x is \frac{1}{x}:


\displaystyle \frac{d (\ln x)}{dx} = \frac{1}{x}


It therefore follows that:

\displaystyle \int \frac{1}{x} = \ln x + c.

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