From powers to the exponential function

We already know about powers: we can compute $a^n$ for natural, negative integer and rational exponents. The new step consists in admitting that $a^x$ makes sense for every real exponent, so that we can speak of a genuine function $\exp_a$. For this function to be “well behaved”, however, the base must be chosen with care: it must be positive and different from $1$.

• From powers to the exponential function
• The conditions on the base