#### Module 4 – Exponential and Logarithmic Functions

### Section 4.4 – Properties of Logarithms

#### Introduction

For the problem introducing the
previous
section, we found that the number of weeks required is log_{1/2} (1/10).
Some
calculators will give this directly as about 3.32 weeks (ie 3 weeks 2
days and
about 6 hours), but even with such calculators it may take longer to
figure out
how to enter it properly than to simplify the expression before
evaluating. In
this section you will learn how to combine and simplify expressions
involving
logarithms and in fact will find that just a single log button is all
you need.

#### What to do

1.
Review
(or just recall to mind) the laws of exponents. For each of these we’ll
get a
translation into the language of logarithms.

2.
Read
section 4.5 of the text using the Reading Guide
as needed.
Keep a pencil and paper at hand, and be sure to check your
understanding by
trying the examples before reading how to do them.

3.
Read
the following Study Notes and Discussion, and
make sure
that you have absorbed the main points by answering the questions.

4.
Follow
the instructions regarding Practice. When you
have met the Learning Objectives for this
Section, go on
to the next.