1. SOLVING LOGARITHMIC EQUATIONS Objective: solve equations with a “log” in them using properties of logarithms How are log properties use to solve for unknown values?

2. Solving Logarithmic Equations  Remember that an exponential and a logarithm are INVERSES of each other.  Which means that they UN-DO each other (cancel out).

3.  log 3 (3 x ) = _______  log 4 (4 2x ) = _______  5 log 5 (x) = ________  3 log 3 (2x) = _______

4.  To solve a logarithmic equation make each side into an EXPONENTIAL equation with the same BASE

5. Ex 1) Solve

6. Ex 2) log 4 (5x + 1) = 2 5x + 1 = 4 2 5x + 1 = 16 5x = 15 x = 3

7. You try!

8.  The common log will not show its base, remember that it is always ____________.

9. Ex 3) Solve

10. Ex 4)

11. You Try!

12.  The natural log will not show its base, remember that it is always _______.

13. Ex 5) Solve

14. Ex 6)

15. You Try!

16. One log each side then… x = y

17. Power Rule

18. Product Property

19. Quotient Property

20. Use properties to re-write  a.  b.  c.  d.

21. Ex 7) One log each side log 5 (-3m – 1) = log 5 (-4m – 6)

22. Ex 8) Power Property 2log(x) = 5

23. Ex 9) Product Property

24. Ex 10) Quotient Property

25. Ex 11) Multiple Properties 4 log 2 (x) + log 2 (5) = log 2 (405)

26. Ex 12) Multiple Properties

27. 1.

28. 2.

29. 3.

30. 4.