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Chapter 3 Exponential and Logarithmic Functions 1
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3.4 Solving Exponential and Logarithmic Equations Objectives: Solve simple exponential and logarithmic equations. Solve more complicated exponential equations. Solve more complicated logarithmic equations. Use exponential and logarithmic equations to model and solve real-life problems. 2
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Change-of-Base Formula Used to convert a log from one base to another. To convert from base a to base b : 3
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Change-of-Base Formula Most commonly used to convert a log to base 10 or to natural log for calculator use. To convert from base a to base 10 : To convert from base a to natural log: 4
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Examples Solve each by converting to common log and then using your calculator. Solve again by converting to natural log. How do the answers compare? 5
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Properties of Logarithms 6
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Properties of Natural Logs 7
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Examples Write each logarithm in terms of ln 2 and ln 3. 8
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Using the Properties Properties of logs are used to rewrite logarithmic expressions, specifically to expand or condense them. Expand – Take a single, complicated log expression and write it as several simple log expressions. Condense – Take several simple log expressions and write them as one log expression. 9
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Examples – Expanding Expressions Use the properties of logarithms to expand each expression. 10
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Examples – Condensing Expressions Use the properties of logarithms to condense each expression. 11
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Additional Examples Given f (x) = ln x, determine whether each statement below is true or false. Justify your answer. 12
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Homework 3.3 Worksheet 3.3 # 5, 11, 15, 23 – 61 odd, 67 – 79 odd, 82, 85 – 91 odd, 103, 105 13
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