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Expontential 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.