1. Worksheet Key
1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

2. 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

3. Exponential and Logarithmic Equations
Section 7.6 – Revised ©2013,
Exponential and Logarithmic Equations
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7.6 - Solving Exp and Log Equations

4. Review Exponent Equations
Product:
Quotient:
Power:
n + m
n – m
n* m
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7.6 - Solving Exp and Log Equations

5. Review Log Equations Product: Quotient: Power: 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

6. Change of Base
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7.6 - Solving Exp and Log Equations

7. CONVERT IT OUT CONVERT When in doubt . . . 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

8. Review Convert 98 – x = 27 to Logarithmic Form 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

9. Solving Exponential Equations
If it is in exponential form, rewrite it in logarithmic form
Apply the Change of Base equation
Solve algebraically, Round to 3 decimal places
Check
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7.6 - Solving Exp and Log Equations

10. Example 1 Solve 98 – x = 27x – 3 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

11. Example 1 Solve 98 – x = 27x – 3 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

12. Example 2 Solve 8x = 2x + 1 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

13. Example 3 Solve 45x = 162x – 1 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

14. Your Turn Solve 9x = 3x – 1 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

15. Example 4 Solve 4x – 1 = 5 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

16. Example 5
Solve 5x = 2
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7.6 - Solving Exp and Log Equations

17. Your Turn Solve 32x–1 = 20 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

18. Solving Logarithmic Equations
If each equation on one side shows a log:
Rewrite the equation in exponential form using
Isolate the variable
Condense the problem
Convert if necessary
Solve algebraically, Round to 3 decimal places. If it is a quadratic, you may use the Quadratic Formula. List all extraneous solutions.
Check
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7.6 - Solving Exp and Log Equations

19. Example 6 Solve log7(5x + 3) = 3 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

20. Example 7 Solve log6(2x – 1) = –1 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

21. Your Turn Solve log5(x – 2) = –1 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

22. Example 8 Solve log4100 – log4(x + 1) = 1 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

23. Example 9
Solve and list all extraneous solutions: log12x + log12(x + 1) = 1
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7.6 - Solving Exp and Log Equations

24. Your Turn Solve log (2x – 1) – log(x – 2) = 1 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

25. Natural Log Equations Product: Quotient: Power: 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

26. Example 10 Solve ln(x – 3) + ln(2x + 1) = 2 ln (x) 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

27. Example 10 Solve ln(x – 3) + ln(2x + 1) = 2 ln (x) 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

28. Example 10 Solve ln(x – 3) + ln(2x + 1) = 2 ln (x) 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

29. Example 11 Solve ln(4x – 1) + ln(x + 2) = 2 ln (x) 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

30. Your Turn Solve ln(x + 2) + ln (2x – 1) = ln x 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

31. Example 12 Solve 5 – ln(x – 3) = ln(x – 3) 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

32. Example 12 Solve 5 – ln(x – 3) = ln(x – 3) 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

33. Your Turn Solve 8 – ln(2x + 1) = ln(2x + 1) 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations

34. Assignment Worksheet 1/2/2019 9:28 PM
7.6 - Solving Exp and Log Equations