## NEKG33 Mathematical methods for economists

## Chapter 5 : Day 05: Power- exponential and logarithmic functions

### By Lund University

Have you had the pleasure of working with logarithms? You may find them a bit nasty, but they are actually quite nice. We will cram in some other stuff as well such as power- and exponential functions.

## Logarithms

We begin the section on logarithms by looking at the common logarithm. Next, we look at the logarithmic identities and the logarithm of a product, a ratio and a power. We move on to the natural logarithm and the rules governing the natural logarithm and we conclude section with logarithms with an arbitrary base.

#### The common logarithm

#### Logarithmic laws for the common logarithm

#### The natural logarithm

#### Logarithm with arbitrary base

## Nonlinear functions

In this section we will look at the most common nonlinear functions. We begin with rational functions followed by power functions, functions where the base in the power is our variable. For the exponential functions, it is the exponent in the power is our variable. This section is concluded with the logarithmic functions.

#### Rational functions

#### Power functions

#### Exponential functions

#### Logarithmic functions

## Problems, Nonlinear functions

Exercises on nonlinear functions.