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.


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.

Problem: Power function

Problem: Exponential function

Problem: Exponential function

Problem: Logarithmic function

Problem: Exponential function

Problem: Logarithmic function

Problem: Logarithm of a product

Problem: Log of a number close to 1

Problem: Logarithm of a power

Problem: Logarithm of an exponential function

Problem: Exponential and logarithmic function

Problem: Logarithm

Problem: Solving equations using log and exp

Problem: Logarithmic laws