Intermediate Algebra – Student Workbook – Second Edition 2013

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$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

Lesson 4a – Introduction to Logarithms Mini-Lesson Why do we care about Logarithms? Logarithms are used in the sciences particularly in biology, astronomy and physics. The Richter scale measurement for earthquakes is based upon logarithms, and logarithms formed the foundation of our early computation tool (pre-calculators) called a Slide Rule. One of the unique properties of Logarithms is their ability to scale numbers of great or small size so that these numbers can be understood and compared. Let’s see how this works with an example. Problem 7 WORKED EXAMPLE – USING LOGARITHMS AS A SCALING TOOL Suppose you are given the following list of numbers and you want to plot them all on the same number line: Plot 0.00000456, 0.00372, 1.673, 1356, 123,045 and 467,456,345,234. If we scale to the larger numbers, then the smaller numbers blend together and we can’t differentiate them. Let’s use logarithms and create a logarithmic scale and see how that works. First, make a table that translates your list of numbers into logarithmic form by taking the “log base 10” or common logarithm of each value. Original # 0.00000456 0.00372 1.673 1356 123,045 467,456,345,234 Log (#) -5.3 -2.4 .2 3.1 5.1 11.7 Then, redraw your number line and plot the logarithmic value for each number. Notice that labeling your scale as a logarithmic scale is VERY important. Otherwise, you may not remember to translate back to the actual data and you may forget that your tick marks are not unit distances. The new scale gives you an idea of the relative distance between your numbers and allows you to plot all your numbers at the same time. To understand the distance between each tick mark, remember that the tick mark label is the exponent on 10 (base of the logarithm used). So from 1 to 2 is a distance of 10 2 - 10 1 = 100 - 10 = 90. The distance between 2 and 3 is 10 3 – 10 2 or 1000 – 100 = 900, etc… You will learn a LOT more about logarithmic scaling if you take science classes, as this is just a very brief introduction to the idea. Scottsdale Community College Page 150 Intermediate Algebra
Lesson 4a – Introduction to Logarithms Mini-Lesson Solving Logarithmic Equations by Changing to Exponential Form We will use what we now know about Logarithmic and Exponential forms to help us solve Logarithmic Equations. There is a step-by-step process to solve these types of equations. Try to learn this process and apply it to these types of problems. Solving Logarithmic Equations – By Changing to Exponential Form Solving logarithmic equations involves these steps: 1. ISOLATE the logarithmic part of the equation 2. Change the equation to EXPONENTIAL form 3. ISOLATE the variable 4. CHECK your result if possible 5. IDENTIFY the final result in EXACT form then in rounded form as indicated by the problem Notes: To ISOLATE means to manipulate the equation using addition, subtraction, multiplication, and division so that the Log part and its input expression are by themselves. EXACT FORM for an answer means an answer that is not rounded until the last step Problem 8 MEDIA EXAMPLE – SOLVING LOGARITHMIC EQUATIONS Solve for x Original Problem Statement Step 1: ISOLATE the logarithmic part of the equation Step 2: Change the equation to EXPONENTIAL form Step 3: ISOLATE the variable Step 4: CHECK your result if possible Step 5: IDENTIFY the final result in EXACT form then in rounded form as indicated by the problem Scottsdale Community College Page 151 Intermediate Algebra
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Scottsdale Community College Interm
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Table of Contents Lesson 1a - Intro
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Lesson 1a - Introduction to Functio
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Lesson 1b - Linear Equations In the
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Lesson 1b - Linear Equations Mini-L
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Lesson 6a - Exponents and Rational
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Lesson 6b - Rational Exponents & Ra
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Appendix A: You Try Answers Lesson
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Appendix A: You Try Answers You Try
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Intermediate Algebra – Student Workbook – Second Edition 2013

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