Thurs, February 26, 2015today’s agenda in

Algebra 21. Quiz2. Notes Unit 10 Lesson 3c3. Assignment Check

Algebra 2 Quiz Today

Unit 10 Lesson 3c:Logarithmic FunctionsCCSS LESSON GOALS

F-LE 4: express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

How are exponential equations and logarithmic equations related?

How is an equation with a missing exponent solved?

ESLRs: Becoming Competent Learners and Complex Thinkers

8xy

8logy x

Example

Find the inverse of the function.

8logx ylogbase

x

xy e ponent

y = b

10xy

logy x

Example

Find the inverse of the function.

10logx ylogbase

x

xy e ponent

y = b

xy e

lny x

Example

Find the inverse of the function.

logex ylogbase

x

xy e ponent

y = b

ln 3y x

Example

Find the inverse of the function.

ln 3x y

3 xy e 3xy e

log 3ex y logbx

y x

y= b

52 logx y

5log 2y x

Example

Find the inverse of the function.

5log 2x y

25 xy

ln 10y x

Example

Find the inverse of the function.

ln 10x y

10xe y

10xy e

Example

The number S of strides per minute at which an animal breaks from a trot to a gallop is related to the animal’s weight w (in pounds) by the model

Approximate the number of strides per minute for a 500 pound horse when it breaks from a trot to a gallop.

256.2 47.9 logS w

256.2 47.9 log500S

2.69897000434256.2 47.9S 256.2 129.280663208S 126.9S

approximately 127 strides per minute

Example

The wind speed S (in miles per hour) near the center of a tornado is related to the distance d (in miles) the tornado travels by the model

Approximate the distance a tornado traveled that has a wind speed of 267 miles per hour.

93log 65S d

267 93log 65d 202 93log d2.17 log d

2.1710d approximately 148 miles

Assignment Check

p. 490: 6 – 12 e, 48 – 55 all

6 8 10 12

48 49 50 51

52 53 54 55

p. 490: 6 – 12 e, 48 – 55 all

3x2xx2x

xxxx

42019 115 5

logbase y exponent

exponentbase y

15 5

logbase y exponent

exponentbase y

019 1

5 25x

2x

log log 4y

4y

5 5log logy x

y x

2 2y x

y x

9 9log logy x

y x

35 35log logy x

y x

24log 4 x

2x

7 7log logy x

y x

2log10 x

2x

320log 20 x

3x

Today’s Assignment

p. 491: 56 – 64 e; 81 (use a calculator or set up the problem, do not graph)