College Algebra, 4th Edition

Section 4.5 Logarithmic Scales; Modeling

Before Starting this Section, Review

1. 1 Exponential form for logarithms (Section 4.2 , page 445)

2. 2 Properties of logarithms (Section 4.2 , page 446)

3. 3 Rules for logarithms (Section 4.3 , page 471)

Objectives

1. 1 Define pH.

2. 2 Define the Richter scale for measuring earthquake intensity.

3. 3 Define scales for measuring sound.

4. 4 Define magnitude of star brightness.

5. 5 Build models from data

A logarithmic scale is a scale in which logarithms are used in the measurement of quantities. Suppose we have a quantity that has a small positive range of variation (for example, from $0.00001={10}^{-5}$ to $0.0001={10}^{-4}$); then ...