Definition:Exponential Function

Let $$e$$ be Euler's number, i.e. $$2.71828\ldots$$

Let $$x \in \mathbb{R}$$ be a real number.

Then from the definition of the power of a real number, $$e^x$$ is defined and has a unique value.

The number $$e^x$$ is called the exponential of $$x$$ and the operation of raising $$e$$ to the power of $$x$$ is known as the exponential function.

The definition still holds when $$x \in \mathbb{C}$$ is a complex number.