Exponential and logarithmic functions

Footnote

²However, note we have not shown this. We have not shown that the limit \(\lim_{h \to 0} \dfrac{a^h - 1}{h}\) is a continuous function of \(a\); otherwise, this limit might never take the value 1. And we have not shown that the limit is a strictly increasing function of \(a\); if not, there might be multiple values of \(a\) for which the limit is 1. The alternative treatment later in this module avoids these issues.