Unit 4

Logarithms

Introduction

Lesson 4.2: Logarithmic Laws and Equations

Can you imagine trying to figure out decimal solutions to logarithmic equations? In Lesson 4.1, you worked with basic logarithmic expressions, equations, and functions to develop an understanding of how logarithms and exponents are related. You evaluated simple logarithms, and you estimated logarithms with decimal values.

Fortunately, technology can assist us in evaluating more complex logarithmic expressions. This is a luxury Napier did not have as he developed logarithms and their laws/rules many centuries ago. However, thanks to Napier, the laws of logarithms, which we will discuss in this Lesson, make calculations far more efficient, even when using a calculator. In fact, the laws of logarithms provide wonderful shortcuts for mathematicians and scientists, even today!

In Lesson 4.2, you will

• explore the logarithmic laws,
• make connections between logarithmic laws and exponent laws,
• apply logarithmic laws,
• solve logarithmic equations,
• verify solutions to logarithmic equations,
• determine extraneous solutions to logarithmic equations, and
• solve problems using logarithmic equations.
  

Coming into this Lesson, you should have

• an understanding of exponential laws and
• the ability to verify solutions to an equation.