Intermediate Algebra – Student Workbook – Second Edition 2013

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

Lesson 4b – More on Logarithms Mini-Lesson Using Calculators to Compute with Bases other than 10 Now that we know something about working with logarithms, let’s see how our calculator can help us with more complicated examples. Problem 2 MEDIA EXAMPLE – INTRODUCING CHANGE OF BASE FORMULA Let’s try to compute log 2 19. To start, let’s estimate values for this number. Try to find the two consecutive (one right after the other) whole numbers that log 2 19 lives between. ____________ < log 2 19 < _____________ ____________ < log 2 19< _____________ So, now we have a good estimate for log 2 19let’s see how our calculator can help us find a better approximation for the number. To compute log 2 19 in your calculator, use the following steps: Log>19)>/Log2)>ENTER and round to three decimals to get: log 2 19= _____________ Do we believe this is a good approximation for log 2 19? How would we check? ____________________ So, our estimation for log 2 19 is good and we can say log 2 19 = __________ with certainty. How did we do that again? We said that log 2 19 = log(19) . How can we do that for any log(2) problem? Change of Base Formula – Converting with Common Logarithms (base 10) log b x = log(x) log(b) Scottsdale Community College Page 164 Intermediate Algebra
Lesson 4b – More on Logarithms Mini-Lesson Problem 3 YOU TRY – COMPUTE LOGARITHMS USING CHANGE OF BASE FORMULA Use the Change of Base formula given on the previous page, and your calculator, to compute each of the following. The first one is done for you. a) log 3 8 Compute b) log 5 41 Rewrite using Change of Base log(8) log(3) Final Result (3 decimal places) – Be sure to use ( ) with each logarithm separately 1.893 c) log 8 12 d) log 1.5 32 e) 12.8+ log 3 25 Solving Exponential Equations Algebraically and Graphically We will use what we now know about Logarithmic and Exponential forms and Change of Base formula to help us solve Exponential Equations. There is a step-by-step process to solve these types of equations. Solving Exponential Equations – Algebraically and Graphically Solving exponential equations involves these steps: ISOLATE the exponential part of the equation Change the equation to LOGARITHMIC form ISOLATE the variable IDENTIFY the final result in EXACT form then in rounded form as indicated by the problem. You may need to use Change of Base here to compute your logarithm. CHECK your result by using the graphing (intersection) method to solve the original problem Notes: To ISOLATE means to manipulate the equation using addition, subtraction, multiplication, and division so that the exponential part and its input expression are by themselves. EXACT FORM for an answer means an answer that is not rounded until the last step. Scottsdale Community College Page 165 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 6a - Exponents and Rational
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Lesson 6b - Rational Exponents & Ra
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Lesson 6b - Rational Exponents and
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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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