Real exponential function/Base/Properties/Fact/Proof/Exercise
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Let denote a positive real number. Prove that the exponential function
fulfills the following properties.
- We have for all .
- We have .
- For and , we have .
- For and , we have .
- For , the function is strictly increasing.
- For , the function is strictly decreasing.
- We have for all .
- For , we have .