1. Unit 2 Logarithms

2. DO NOW Expand the logarithm and simplify if possible Log 5 32 x
Answer: 2 log 5 3 – log 5 x

3. activating

4. 7 – 4 Objective: Understand the properties of logarithms
Objective: expand and condense logarithmic expressions
Objective: Change of base formula

5. examples Reasoning: Can you expand log 3 (2x + 1) ? Explain
No, the expression (2x + 1) is a sum, so it is not covered by the product, quotient, or power properties
2. Write the logarithmic expression as a single logarithm :1/2 ( log x 4 + log x y) – 3 log x z
Log x 2√ y
z 3

6. More examples for you to try
Write each logarithm as the quotient of 2 common logarithms. Do not simplify the quotient
Pg. 467 #68, 69
(hint log answer/log base)
Evaluate each logarithm
Pg. 468 # 93
Pg 468 # 54

7. One more problem
What is the value of log 7 25? Use the change of base formula
About 1.65

8. worksheets
7 -4 think about a plan
7 -4 puzzle: letter scramble

9. 7-5, 7-6, and polynomials

10. Do now
Pg. 461 #22
Pg. 467 #70 and 72
Pg. 473 # 7

11. 7 - 5 How can you solve exponential equations?
Objective: solve logarithmic equations using technology and algebraically

12. Exponential equation Any equation that contains the form bcx, as
a = bcx, where the exponent includes a variable
Remember, you can use LOGARITHMS to solve exponential equations
You can use EXPONENTS to solve logarithmic equations

13. examples Solving an exponential equation – common base Pg. 469
Finding solutions
Use power property of exponents to solve

14. examples Solving an exponential equation – different bases
Finding solutions
Solve by taking logarithm of each side of the equation

15. Solving an exponential equation with graph or table

16. Modeling with exponential equations
Logarithmic equation: is an equation that includes one or more logarithms involving a variable
Pg. 477

17. Using logarithmic properties to solve an equation

18. Solving a logarithmic equation
Problems in book and worksheet

19. H.O.T. question/activity/task
Given y = ab cx
Explain how replacing c with ( - c ) affects the function

20. Wrap up
How are logarithms and exponential functions related to real-world data? (actual events, weather, money, etc). In your answer identify behaviors that tend to be explained using logarithmic and exponential functions (use the terms learned)
Answers: radioactivity, hurricanes, population growth, stock market, compound interest

21. Doubling time discovery
Test thursday unit 2, complete or try to finish review packet

22. 7-6 Natural logarithms pg. 478
The function y = ex has an inverse, the natural logarithmic function, y = logex, or y = ln x
Y = ex and y = ln x are inverse functions
a = eb then b = ln a

23. Log vs LN
Sometimes it is easier to think of logs in these terms instead! So, the difference is in the base -- ln has base e, log has base 10.
The log button on your calculator is known as the common logarithm which is of base 10. The ln button on your calculator has a base of "e". Here is what they look like: Base 10 y = log(10) x Natural Base y = log(e)x Written as y = ln x There are a couple of reasons why we use the natural logarithm versus the logarithm of base, b. When dealing with log, there are 2 variables that can affect the function, the base and the x value. With ln, since the base is always "e", the only factor affecting the function is x. It just makes it easier to manipulate and use mathematically. 

25. Begin unit 3
Unit 3 diagnostic test
Homework if don’t get too

26. Unit 3 Polynomials

27. Agenda
Do now
Activating
What’s up next?

28. What you will be able to do?
Factor polynomials
Describe end behavior of polynomials
Find the inverse of functions
Know and apply the binomial theorem
Recognize a polynomial function in real-world situation
What does the degree of a polynomial tell you about its related polynomial function?

29. Vocabulary Zeroes Binomial expansion Multiplicity Relative extrema
concavity

30. Operations of polynomials
Add, subtract, multiply polynomials
Synthetic division
Remainder theorem

31. Operations of polynomial problems

32. Binomial expansion
Pascal’s triangle

33. Binomial
Examples:

34. H.O.T. Question
Why do we need Pascal Triangle? What is it used for?

35. Rewrite expressions Factoring by GCF
Factoring trinomials (leading coefficients)
Factoring sum & difference of cubes

36. examples

37. Terms and examples
Zeroes, quadratics, roots, end behaviors, radicals

38. Rational root theorem

39. Higher degree functions
Example and definitions

40. Wrap up