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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities Solve exponential and logarithmic equations and equalities. Solve problems involving exponential and logarithmic equations. Objectives

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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities exponential equation logarithmic equation Vocabulary

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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities An exponential equation is an equation containing one or more expressions that have a variable as an exponent. To solve exponential equations: Try writing them so that the bases are all the same. Take the logarithm of both sides.

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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities When you use a rounded number in a check, the result will not be exact, but it should be reasonable. Helpful Hint

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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities Solve and check. 3 2x = 27 Check It Out! Example 1a

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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities Solve and check. 7 –x = 21 Check It Out! Example 1b

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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities Solve and check. 2 3x = 15 Check It Out! Example 1c

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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities You receive one penny on the first day, and then triple that (3 cents) on the second day, and so on for a month. On what day would you receive a least a million dollars. Check It Out! Example 2

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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities A logarithmic equation is an equation with a logarithmic expression that contains a variable. You can solve logarithmic equations by using the properties of logarithms.

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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities Review the properties of logarithms from Lesson 7-4. Remember!

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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities Solve. 3 = log 8 + 3log x Check It Out! Example 3a

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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities Solve. 2log x – log 4 = 0 Check It Out! Example 3b

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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities Watch out for calculated solutions that are not solutions of the original equation. Caution

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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities In the table, find the x-values where Y1 is equal to Y2. In the graph, find the x-value at the point of intersection. Check It Out! Example 4a Use a table and graph to solve 2 x = 4 x – 1. Use a graphing calculator. Enter 2 x as Y1 and 4 (x – 1) as Y2. The solution is x = 2.

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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities In the table, find the x-values where Y1 is greater than Y2. In the graph, find the x-value at the point of intersection. Check It Out! Example 4b Use a table and graph to solve 2 x > 4 x – 1. Use a graphing calculator. Enter 2 x as Y1 and 4 (x – 1) as Y2. The solution is x < 2.

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Holt McDougal Algebra Exponential and Logarithmic Equations and Inequalities In the table, find the x-values where Y1 is equal to Y2. In the graph, find the x-value at the point of intersection. Check It Out! Example 4c Use a table and graph to solve log x 2 = 6. Use a graphing calculator. Enter log(x 2 ) as Y1 and 6 as Y2. The solution is x = 1000.

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