Five-Minute Check (over Lesson 8–3)

Then/Now

New Vocabulary

Example 1: Solve a Logarithmic Equation

Key Concept: Property of Equality for Logarithmic Functions

Example 2: Standardized Test Example

Key Concept: Property of Inequality for Logarithmic Functions

Example 3: Solve a Logarithmic Inequality

Key Concept: Property of Inequality for Logarithmic Functions

Example 4: Solve Inequalities with Logarithms on Each Side

Over Lesson 8–3

A. A

B. B

C. C

D. D A B C D

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Write 4–3 = in logarithmic form.__164

A. log–3 4 =

B. log–3 = 4

C. log4 = –3

D. log4 –3 =

__1

64

__1

64

__1

64

__1

64

Over Lesson 8–3

A. A

B. B

C. C

D. D A B C D

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Write log6 216 = 3 in exponential form.

A. 63 = 216

B. 36 = 216

C.

D.

Over Lesson 8–3

A. A

B. B

C. C

D. D A B C D

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A. x – 4

B. x – 2

C. 4x – 2

D. 4x – 1

Evaluate 4log4 (x – 2).

Over Lesson 8–3

A. A

B. B

C. C

D. D A B C D

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Graph f(x) = 2 log2 x.

C.

D.

A. ans

B. ans

Over Lesson 8–3

A. A

B. B

C. C

D. D A B C D

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Graph f(x) = log3 (x – 4).

A.

B.

C.

D.

Over Lesson 8–3

A. A

B. B

C. C

D. D A B C D

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A.

B.

C.

D.

You evaluated logarithmic expressions. (Lesson 8–3)

• Solve logarithmic equations.

• Solve logarithmic inequalities.

• logarithmic equation

• logarithmic inequality

Solve a Logarithmic Equation

Answer: x = 16

Original equation

Definition of logarithm

8 = 23

Power of a Power

Solve

A. A

B. B

C. C

D. D A B C D

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Solve .

A.

B. n = 3

C. n = 9

D.

n =

n =

Solve log4 x

2 = log4 (–6x – 8).

A. 4 B. 2 C. –4, –2 D. no solutions

Read the Test ItemYou need to find x for the logarithmic equation.

Solve the Test Item

log4 x

2 = log4 (–6x – 8) Original equation

x

2 = (–6x – 8) Property of Equality for LogarithmicFunctions

x

2 + 6x + 8 = 0 Subtract (–6x – 8)from each side.

(x + 4)(x + 2) = 0 Factor.

x + 4 = 0 or x + 2 = 0 Zero ProductProperty

x = –4 x = –2 Solve each equation.

x = –4

log4 (–4)2 = log4 [–6(–4) – 8)]

log4 16 = log4 16

x = –2

log4 (–2)2 = log4 [–6(–2) – 8)]

log4 4 = log4 4

Check

Substitute each value into the original equation.

Answer: The solutions are x = –4 and x = –2.The answer is C.

A. A

B. B

C. C

D. D A B C D

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A. 5 and –4

B. –2 and 10

C. 2 and –10

D. no solutions

Solve log4 x

2 = log4 (x + 20).

Solve a Logarithmic Inequality

Solve log6 x > 3.

log6 x> 3 Original inequality

x > 63 Property of Inequality for Logarithmic Functions

x > 216 Simplify.

Answer: The solution set is {x | x > 216}.

A. A

B. B

C. C

D. D A B C D

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A. {x | x < 9}

B. {x | 0 < x < 9}

C. {x | x > 9}

D. {x | x < 8}

What is the solution to log3 x < 2?

Solve Inequalities with Logarithms on Each Side

Solve log7 (2x + 8) > log7 (x + 5).

log7 (2x + 8) >log7 (x + 5)Original inequality

2x + 8 > x + 5Property of Inequality for Logarithmic Functions

x > –3Simplify.

Answer: The solution set is {x | x > –3}.

A. A

B. B

C. C

D. D A B C D

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Solve log7 (4x + 5) < log7 (5x + 1).

A.

B.

C.

D.

{x | x > 4}

{x | x ≥ 4}

{x | 0 < x < 4}