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# Exponential functions

Exponential functions are Functions with the form $$f(x) = b^x$$, where $$b > 0$$ and $$b \neq 1$$.

They are the inverse of Logarithmic functions.

## Identities

$b^x b^y = b^{x+y}$ $\frac{b^x}{b^y} = b^{x-y}$ $(b^x)^y = b^{xy}$ $(ab)^x = a^x b^x$ $(\frac a b)^x = \frac{a^x}{b^x}$ $b^{-x} = \frac{1}{b^x}$

## Properties

The range is always $$(0, \infty)$$.

When $$b > 1$$ the function is increasing.

If $$b < 1$$ the function is decreasing.