## Logarithms and exponentials.

The logarithms and the exponentials can be defined in many ways. Precise definitions and proofs are given in Appendix I (i.e. chapter logs-exp).

Proposition 4.5.9
 Logarithms Exponentials

As an application, let us compute the limit, if it exists, of for arbitrary large. Note that we have here a situation of the type described above in subsection subsubsection Numerator and denominator have both an infinite limit.

As and , we have: .

Note that there are other ways to solve this question; one of them will appear with L'Hopital's rule (Theorem L'Hopital), another one with Taylor polynomials (v.i. Def. Taylor polynomials).

Noah Dana-Picard 2007-12-28