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Graphing logarithmic and exponential functions

The Exponential function as the inverse of the logarithmic function

Graphically, an inverse function is one which appears to be reflected along the \( y = x \) line.

For example, if we plotted on the same set of axes:

  • \(y = \log_{2}(x)\)
  • \(y = 2^x \) and
  • the line \( y = x \)

we have:

  • The logarithmic function is an inverse of the exponential growth function so all of its properties are mirror image (reflected in the line \(y=x\)) of the properties of the exponential growth function.