Grade 11 · Math · Algebra 2

11th grade Properties of logarithms: product, quotient and power, expanding and condensing worksheet

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Properties of logarithms: product, quotient and power, expanding and condensing

Grade 11 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

In Jun's × 3 growth table, 9 is row 2 and 27 is row 3. What is log₃ (9 × 27)?
In Kira's × 2 growth table, 4 is row 2 and 32 is row 5. What is log₂ (4 × 32)?
In Milo's × 3 growth table, 2187 is row 7 and 9 is row 2. What is log₃ (2187 ÷ 9)?
Pia knows that log 1000 = 3. What is log (1000²)?
Ren knows that log₂ 16 = 4. What is log₂ (16³)?
6.
Tala expands log₅ (7x) on a math club card. Which choice is equal to log₅ (7x)?
- log₅ 7 − log₅ x
- log₅ 7 · log₅ x
- 7 log₅ x
- log₅ 7 + log₅ x
7.
Zee expands log₃ (x/4) in a math book. Which choice is equal to log₃ (x/4)?
- log₃ x ÷ log₃ 4
- log₃ x + log₃ 4
- log₃ x − log₃ 4
- log₃ 4 − log₃ x
8.
Ari expands log₂ (x⁵) on the class board. Which choice is equal to log₂ (x⁵)?
- x log₂ 5
- (log₂ x)⁵
- 5 log₂ x
- log₂ (5x)
9.
Bo writes log₂ x + log₂ 5 as one log on a math club card. Which choice is it?
- (log₂ x)(log₂ 5)
- log₂ (x/5)
- log₂ (x + 5)
- log₂ (5x)
10.
Jun writes 3 log₅ x as one log on the class board. Which choice is it?
- log₅ (x³)
- log₅ (x + 3)
- log₅ (3x)
- (log₅ x)³

11th grade Properties of logarithms: product, quotient and power, expanding and condensing worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Properties of logarithms: product, quotient and power, expanding and condensing. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can say why multiplying inside a log adds the logs, dividing subtracts them, and a power multiplies the log.
I can expand a log of a product, quotient or power, and keep the log of a sum whole.
I can write a sum of logs with numbers in front as one log, and find a log from given values.

Standard: no CCSS standard names them (F-BF.B.5 (+) is nearest)

Words to know

product rule: log (MN) = log M + log N: multiplying results adds rows.

quotient rule: log (M/N) = log M − log N: dividing results subtracts rows.

power rule: log (Mⁿ) = n log M: a power multiplies the row.

expand: Write one log of a product, quotient or power as several logs.

condense: Write several logs with one base as one log.

row: The step number in the growth table; for a result, its log.

Common mistakes

Multiplied two logs where they should be added. Write 4 × 8 = 32 as 2² × 2³ = 2⁵ together and see the powers add.

Divided two logs where they should be subtracted. Write 32 ÷ 4 as 2⁵ ÷ 2² = 2³ together and see the powers subtract.

Subtracted the logs in the wrong order.

What to say

Ask: which number is on top of the fraction? Its log comes first.

Questions parents ask

What is the most common mistake with properties of logarithms: product, quotient and power, expanding and condensing?

Multiplied two logs where they should be added. Write 4 × 8 = 32 as 2² × 2³ = 2⁵ together and see the powers add.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 2

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