1. W ARM U P

2. L OGARITHMIC F UNCTIONS SWBAT identify key features and apply properties of logarithmic functions. Given 2 MC and 2 CR problems, students will identify key features and apply properties of logarithmic functions with 80% accuracy. ObjectiveDOL

3. H OW ARE LOGARITHMS AND EXPONENTIALS RELATED ? Essential Question

4. L OGARITHMIC TO E XPONENTIAL … y = log b x 0 = log 8 1 1 = 8 0 y = log b x -4 = log 2 (1/16) 1/16 = 2 -4 0 = log 8 1-4 = log 2 (1/16)

5. Q UICK P RACTICE

7. E XPONENTIAL TO L OGARITHMIC … y = log b x 3 = log 10 1000 y = log b x 1/2 = log 9 3 10 3 = 10009 1/2 = 3

8. E VALUATING LOG AND LN ON THE C ALCULATOR Use ln (natural log (base e)) Use log button (common log (base 10)) There isn’t a base 5 button, so… ?

9. C HANGE OF B ASE F ORMULA This will allow us to evaluate a logarithm with any base!

10. C HANGE OF B ASE F ORMULA Practice

11. E VALUATE.

12. P ROPERTIES OF L OGARITHMS Think-Pair-Share: Why do these look familiar? How can we remember them?

13. P ROPERTIES OF L OGS /E XPONENTS Think/Pair/Share – What do these properties have in common with Properties of Exponents? Explain your thinking..

14. P ROPERTIES OF L OGS /E XPONENTS Think/Pair/Share – What do these properties have in common with Properties of Exponents? Explain your thinking..

15. P ROPERTIES OF L OGS /E XPONENTS Think/Pair/Share – What do these properties have in common with Properties of Exponents? Explain your thinking.

16. C HANGE OF B ASE /E XPAND /C ONDENSE Practice rewriting several logarithmic expressions using the properties (both expanding and collapsing):

17. W HICH PROPERTIES CAN YOU USE TO SIMPLIFY EACH ?

18. R EWRITE -E XPAND -C ONDENSE P RACTICE

19. G IVEN LOG 3 = 0.4771, LOG 4 = 0.6021, AND LOG 5 = 0.6990 Use the properties of logarithms to evaluate each expression. Show your work for each step. Example: log 12 log 12 = log 3(4) = log 3 + log 4 = 0.4772 + 0.6021 = 1.0793

20. G IVEN LOG 3 = 0.4771, LOG 4 = 0.6021, AND LOG 5 = 0.6990 Use the properties of logarithms to evaluate each expression. Show your work for each step. 1. log 16 2. log 3/5 3. log 75 4. log 60

21. S OLVING E XPONENTIAL AND L OGARITHMIC E QUATIONS Practice

22. A PPLICATION a) What property will be used to solve this equation? Will you expand or condense? Power Property

23. A PPLICATION a) What property will be used to solve this equation? Will you expand or condense? Power Property

24. A PPLICATION

25. a) What property will be used to solve this equation? Will you expand or condense? Power Property

26. A PPLICATION a) What property will be used to solve this equation? Will you expand or condense? Power Property

27. A PPLICATION Explain what happens in each step: Substitute in 300 Subtract 5 from both sides Convert to log form Change of base formula Solution

28. A PPLICATION a) What property will be used to solve this equation? Will you expand or condense? Power Property

29. W HAT IS A LOGARITHM ? a number for a given base is the exponent to which the base must be raised in order to produce the number

30. C OMPLETE THE TABLE AND GRAPH THE E XPONENTIAL F UNCTION

31. W HAT ARE THE KEY FEATURES ? Domain: Range: Y-intercept: X-intercept: Asymptote: End behavior: All real numbers All positive numbers; y > 0 (0, 1) No x-intercept y = 0

32. N OW G RAPH THE I NVERSE

33. W HAT ARE THE KEY FEATURES ? Domain: Range: Y-intercept: X-intercept: Asymptote: x > 0 All real number No y-intercept (1, 0) x = 0

34. B ACK TO THE INVERSE

35. H OW ARE LOGARITHMS AND EXPONENTIALS RELATED ? Essential Question

36. DOL #1

37. DOL #2

38. DOL #3 Apply properties of logs to expand this logarithm and explain your reasoning.

39. DOL #4 Maryville was founded in 1950. At that time, 500 people lived in the town. The population growth in Maryville follows the equation, where t is the number of years since 1950. a)Determine when the population had doubled since the founding. b) In what year was the population predicted to reach 25,000 people? c) What social implications could the population growth in that number of years have on the town?

40. DOL Maryville was founded in 1950. At that time, 500 people lived in the town. The population growth in Maryville follows the equation, where t is the number of years since 1950. a)Determine when the population had doubled since the founding. t = 15.327 years so 1965 b) In what year was the population predicted to reach 25,000 people? t = 24.926 so 1974.9 Right before 1975 c) What social implications could the population growth in that number of years have on the town? Jobs, housing, schools, traffic, etc.