### Section 4.4 – Properties of Logarithms

#### Introduction

For the problem introducing the previous section, we found that the number of weeks required is log1/2 (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.