1. Splash Screen

2. Lesson Menu Five-Minute Check (over Lesson 8–3) Then/Now New Vocabulary Example 1: Solve a Logarithmic Equation Key Concept: Property of Equality for Logarithmic Functions Example 2: Standardized Test Example 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

3. Over Lesson 8–3 A.A B.B C.C D.D 5-Minute Check 1 Write 4 –3 = in logarithmic form. __ 1 64 A.log –3 4 = B.log –3 = 4 C.log 4 = –3 D.log 4 –3 = __ 1 64 __ 1 64 __ 1 64 __ 1 64

4. Over Lesson 8–3 A.A B.B C.C D.D 5-Minute Check 2 Write log 6 216 = 3 in exponential form. A.6 3 = 216 B.3 6 = 216 C. D.

5. Over Lesson 8–3 A.A B.B C.C D.D 5-Minute Check 3 A.x – 4 B.x – 2 C.4x – 2 D.4x – 1 Evaluate 4log 4 (x – 2).

6. Over Lesson 8–3 A.A B.B C.C D.D 5-Minute Check 4 Graph f(x) = 2 log 2 x. C. D. A.ans B.ans

7. Over Lesson 8–3 A.A B.B C.C D.D 5-Minute Check 5 Graph f(x) = log 3 (x – 4). A. B. C. D.

8. Over Lesson 8–3 A.A B.B C.C D.D 5-Minute Check 6 A. B. C. D.

9. Then/Now You evaluated logarithmic expressions. (Lesson 8–3) Solve logarithmic equations. Solve logarithmic inequalities.

10. Vocabulary logarithmic equation logarithmic inequality

11. Example 1 Solve a Logarithmic Equation Answer: x = 16 Original equation Definition of logarithm 8 = 2 3 Power of a Power Solve

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

13. Concept

14. Example 2 Solve log 4 x 2 = log 4 (–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 log 4 x 2 =log 4 (–6x – 8)Original equation x 2 =(–6x – 8)Property of Equality for Logarithmic Functions

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

16. Example 2 x = –4 log 4 (–4) 2 =log 4 [–6(–4) – 8)] log 4 16 =log 4 16 x = –2 log 4 (–2) 2 =log 4 [–6(–2) – 8)] log 4 4 =log 4 4 Check Substitute each value into the original equation. Answer:The solutions are x = –4 and x = –2. The answer is C.

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

18. Concept

19. Example 3 Solve a Logarithmic Inequality Solve log 6 x > 3. log 6 x> 3Original inequality x> 6 3 Property of Inequality for Logarithmic Functions x> 216Simplify. Answer: The solution set is {x | x > 216}.

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

21. Concept

22. Example 4 Solve Inequalities with Logarithms on Each Side Solve log 7 (2x + 8) > log 7 (x + 5). log 7 (2x + 8) >log 7 (x + 5)Original inequality 2x + 8 >x + 5Property of Inequality for Logarithmic Functions x >–3Simplify. Answer: The solution set is {x | x > –3}.

23. A.A B.B C.C D.D Example 4 Solve log 7 (4x + 5) < log 7 (5x + 1). A. B. C. D. {x | x > 4} {x | x ≥ 4} {x | 0 < x < 4}

24. End of the Lesson