1. Keeper #39 Solving Logarithmic Equations and Inequalities

2. Solving Exponential Equations
Review

3. Solving Exponential Equations
Review

4. Solving Exponential Equations
Isolate the term with the variable.
On both sides, take the log with the same base as the exponential term.
Simplify using change of base and solve.

5. Solving Exponential Equations

6. Rewriting Equations to Solve

7. Solving Exponential Equations

8. Solving Exponential Equations

9. Solving Exponential Equations

10. Solving Exponential Equations

11. Solving Exponential Equations

12. Solving Exponential Equations

13. Solving Logarithmic Equations
Isolate the logarithm.
Write in exponential form (inverse property).
Solve for the variable.

14. Solving Logarithmic Equations

15. Solving Logarithmic Equations

16. Solving Logarithmic Equations

17. Solving Logarithmic Equations

18. Solving Logarithmic Equations

19. Solving Logarithmic Equations

20. Solving Logarithmic Equations

21. Solving Logarithmic Equations
Sometimes we have to condense first!!

22. Solving Logarithmic Equations

23. Solving Logarithmic Equations

24. Logarithmic Inequalities
Steps:
Create and solve the inequality as normal by converting to exponent form.
Take the expression of the logarithm and determine where the value is greater than 0. This will create the bound of the equation.
Compare the two inequalities and determine if the boundary is needed for the inequality solution.

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29. Example