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Splash Screen. Five-Minute Check (over Lesson 7–3) CCSS Then/Now New Vocabulary Example 1: Solve a Logarithmic Equation Key Concept: Property of Equality for Logarithmic Functions Example 2: Standardized Test Example: Solve a Logarithmic Equation

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 7–3) CCSS Then/Now New Vocabulary Example 1: Solve a Logarithmic Equation Key Concept: Property of Equality for Logarithmic Functions Example 2: Standardized Test Example: Solve a Logarithmic Equation Key Concept: Property of Inequality for Logarithmic Functions Example 3: Solve a Logarithmic Inequality Key Concept: Property of Inequality for Logarithmic Functions Example 4: Solve Inequalities with Logarithms on Each Side Lesson Menu

  3. 1 __ Write 4–3 = in logarithmic form. 64 A.log–3 4 = B.log–3 = 4 C.log4 = –3 D.log4 –3 = 1 1 1 1 __ __ __ __ 64 64 64 64 5-Minute Check 1

  4. 1 __ Write 4–3 = in logarithmic form. 64 A.log–3 4 = B.log–3 = 4 C.log4 = –3 D.log4 –3 = 1 1 1 1 __ __ __ __ 64 64 64 64 5-Minute Check 1

  5. A.63 = 216 B.36 = 216 C. D. Write log6 216 = 3 in exponential form. 5-Minute Check 2

  6. A.63 = 216 B.36 = 216 C. D. Write log6 216 = 3 in exponential form. 5-Minute Check 2

  7. A. ans B. ans C. D. Graph f(x) = 2 log2x. 5-Minute Check 3

  8. A. ans B. ans C. D. Graph f(x) = 2 log2x. 5-Minute Check 3

  9. A. B. C. D. Graph f(x) = log3 (x – 4). 5-Minute Check 4

  10. A. B. C. D. Graph f(x) = log3 (x – 4). 5-Minute Check 4

  11. A. B. C. D. 5-Minute Check 5

  12. A. B. C. D. 5-Minute Check 5

  13. Content Standards A.SSE.2 Use the structure of an expression to identify ways to rewrite it. A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Mathematical Practices 4 Model with mathematics. CCSS

  14. You evaluated logarithmic expressions. • Solve logarithmic equations. • Solve logarithmic inequalities. Then/Now

  15. logarithmic equation • logarithmic inequality Vocabulary

  16. Solve Original equation Definition of logarithm 8 = 23 Power of a Power Solve a Logarithmic Equation Answer: Example 1

  17. Solve Original equation Definition of logarithm 8 = 23 Power of a Power Solve a Logarithmic Equation Answer:x = 16 Example 1

  18. Solve . n = A. B.n =3 C.n =9 D. n = Example 1

  19. Solve . n = A. B.n =3 C.n =9 D. n = Example 1

  20. Concept

  21. Solve a Logarithmic Equation Solve log4 x2 = log4 (–6x – 8). A. 4 B. 2 C. –4, –2 D. no solutions Read the Test Item You need to find x for the logarithmic equation. Solve the Test Item log4 x2 = log4 (–6x – 8) Original equation x2 = (–6x – 8) Property of Equality for Logarithmic Functions Example 2

  22. Solve a Logarithmic Equation x2 + 6x + 8 = 0 Subtract (–6x – 8) from each side. (x + 4)(x + 2) = 0 Factor. x + 4 = 0 or x + 2 = 0 Zero Product Property x = –4 x = –2 Solve each equation. Example 2

  23. ? log4 (–4)2 = log4 [–6(–4) – 8)] ? log4 (–2)2 = log4 [–6(–2) – 8)] Solve a Logarithmic Equation Check Substitute each value into the original equation. x = –4 log4 16 = log4 16  x = –2 log4 4 = log4 4  Answer: Example 2

  24. ? log4 (–4)2 = log4 [–6(–4) – 8)] ? log4 (–2)2 = log4 [–6(–2) – 8)] Solve a Logarithmic Equation Check Substitute each value into the original equation. x = –4 log4 16 = log4 16  x = –2 log4 4 = log4 4  Answer: The solutions are x = –4 and x = –2. The answer is C. Example 2

  25. Solve log4 x2 = log4 (x + 20). A. 5 and –4 B. –2 and 10 C. 2 and –10 D. no solutions Example 2

  26. Solve log4 x2 = log4 (x + 20). A. 5 and –4 B. –2 and 10 C. 2 and –10 D. no solutions Example 2

  27. Concept

  28. Solve a Logarithmic Inequality Solve log6 x > 3. log6x > 3 Original inequality x > 63 Property of Inequality for Logarithmic Functions x > 216 Simplify. Answer: Example 3

  29. Solve a Logarithmic Inequality Solve log6 x > 3. log6x > 3 Original inequality x > 63 Property of Inequality for Logarithmic Functions x > 216 Simplify. Answer: The solution set is {x | x > 216}. Example 3

  30. What is the solution to log3 x < 2? A. {x | x < 9} B. {x | 0 < x < 9} C. {x | x > 9} D. {x | x < 8} Example 3

  31. What is the solution to log3 x < 2? A. {x | x < 9} B. {x | 0 < x < 9} C. {x | x > 9} D. {x | x < 8} Example 3

  32. Concept

  33. Solve Inequalities with Logarithms on Each Side Solve log7 (2x + 8) > log7 (x + 5). log7 (2x + 8) > log7 (x + 5) Original inequality 2x + 8 > x + 5 Property of Inequality for Logarithmic Functions x > –3 Simplify. Answer: Example 4

  34. Solve Inequalities with Logarithms on Each Side Solve log7 (2x + 8) > log7 (x + 5). log7 (2x + 8) > log7 (x + 5) Original inequality 2x + 8 > x + 5 Property of Inequality for Logarithmic Functions x > –3 Simplify. Answer: The solution set is {x | x > –3}. Example 4

  35. {x | x > 4} A. B. C. D. {x | x ≥ 4} {x | 0< x < 4} Solve log7 (4x + 5) < log7 (5x + 1). Example 4

  36. {x | x > 4} A. B. C. D. {x | x ≥ 4} {x | 0< x < 4} Solve log7 (4x + 5) < log7 (5x + 1). Example 4

  37. End of the Lesson

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