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Real exponential function/Base/Properties/Fact

From Wikiversity

Let denote a positive real number. Then the exponential function

fulfills the following properties.

  1. We have for all .
  2. We have .
  3. For and , we have .
  4. For and , we have .
  5. For , the function is strictly increasing.
  6. For , the function is strictly decreasing.
  7. We have for all .
  8. For , we have .