8. SAS 4 Log Properties

Logarithm Properties (Page 6)

Zero Property

​Page 6

Fill in the Blanks

Page 6 Example

$\log_21=$

Open Ended

Page 6 Description

In your own words, describe the zero property.

Identity Property

​Page 6

Fill in the Blanks

Page 6 Example

$\log_22=$

Open Ended

Page 6 Description

In your own words, describe the identity property.

Product Rule Property

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​Page 6

Fill in the Blanks

Page 6 Example

$\log_26+\log_28=\log_2$

Open Ended

Page 6 Description

In your own words, describe the product rule property.

Quotient Rule Property

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​Page 6

Fill in the Blanks

Page 6 Example

$\log_264-\log_28=\log_2$

Open Ended

Page 6 Description

In your own words, describe the quotient rule property.

Power Rule Property

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​Page 6

Fill in the Blanks

Page 6 Example

$4\cdot\log_42=\log_4$

Open Ended

Page 6 Description

In your own words, describe the power rule property.

Multiple Choice

Not in packet

Condense

$$\log_35+\log_34$$  

• $$\log_39$$  

• $$\log_320$$  

• $$\log_69$$  

• $$\log_620$$  

Multiple Choice

Not in packet

Expand

$$\log_28y$$  

• $$\log_82+\log_8y$$  

• $$\log_28+\log_2y$$  

• $$\log_2y+\log_82$$  

• $$\log_y2+\log_y8$$  

Multiple Choice

Not in packet

Condense

$$\log_7y-\log_79$$  

• $$\log_7\frac{9}{y}$$  

• $$\log_79y$$  

• $$\log_7\frac{y}{9}$$  

• $$\log_9\frac{y}{7}$$  

Multiple Choice

Not in packet

Expand

$$\log_4\frac{y}{10}$$  

• $$\log_4y+\log_410$$  

• $$\log_410-\log_4y$$  

• $$\log_{10}y-\log_{10}4$$  

• $$\log_4y-\log_410$$  

Multiple Choice

Not in packet

Condense

$$3\log_47$$  

• $$\log_47^3$$  

• $$\log_421$$  

• $$\log_43^7$$  

• $$\log_410$$  

Multiple Choice

Not in packet

Expand

$$\log_2^{ }y^5$$  

• $$y\cdot\log_25$$  

• $$5\log_2y$$  

• $$2\cdot\log_5y$$  

• $$\log_25^y$$  

Multiple Choice

Page 7 #1

Rewrite the expression log(3x) as an equivalent logarithm expression using only addition.

• $$\log\ 3+x$$

• $$\log\ 3+\log x$$

• $$\log\ 3-x$$

• $$\log3-\log x$$

Multiple Choice

Page 7 #2

Rewrite the expression $$\log_4\left(\frac{10}{4}\right)$$ as an equivalent logarithm expression using only subtraction.

• $$\log_4\ 10+y$$

• $$\log_4\ 10+\log_4y$$

• $$\log_4\ 10-y$$

• $$\log_410-\log_4y$$

Math Response

Page 7 #3 First Box

Apply the properties of logarithms to simplify each expression.

$$\log_x\left(27\right)-\log_x\left(3\right)=$$

Type answer here

Correct Answer: \log_x\left(9\right)

Deg^°

Rad

Multiple Select

Page 7 #3 Second Box

Apply the properties of logarithms to simplify each expression.

$$\log_{10}\left(2\right)+\log_{10}\left(5\right)=$$

• $$\log_{10}10$$

• 1

• $$\log_{10}7$$

Multiple Select

Page 7 #3 Third Box

Apply the properties of logarithms to simplify each expression.

$$\log\left(\frac{2}{x}\right)+\log\left(\frac{x}{2}\right)=$$

• $$\log\left(2x\right)^2$$

• $$\log2-\log x+\log x-\log2$$

• 0

Page 7 #4 a, b, & c

Page 7 #5 First Box

Math Response

$$\log_2\left(\frac{5}{7}\right)$$

Type answer here

Correct Answer: -0.485

Deg^°

Rad

Math Response

$$\log_225$$

Type answer here

Correct Answer: 4.644

Deg^°

Rad

Look at the board for some answers as you are working through page 8

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Classwork - Page 8