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

NameDate

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

Kira works out log₆ 4 + log₆ 9 on the class board. What is log₆ 4 + log₆ 9?
Milo works out log₃ 54 − log₃ 2 on the class board. What is log₃ 54 − log₃ 2?
Noah uses log 2 ≈ 0.301 and log 3 ≈ 0.477 from a math book. To the nearest thousandth, what is log 6?
Ren uses log 2 ≈ 0.301 and log 3 ≈ 0.477 from a math book. To the nearest thousandth, what is log 1.5?
Tala uses log 3 ≈ 0.477 and log 5 ≈ 0.699 from a math book. To the nearest thousandth, what is log 0.6?
Zee uses log 3 ≈ 0.477 from a math book. To the nearest thousandth, what is log 9?
Bo uses log 2 ≈ 0.301 from a math book. To the nearest thousandth, what is log 8?
8.
Esme expands log₂ (8x³/y) fully on a math club card. Which choice is equal to it?
- 3 + 3 log₂ x − log₂ y
- 3 + 3 log₂ x + log₂ y
- (3 + 3 log₂ x) ÷ log₂ y
- 3 + (log₂ x)³ − log₂ y
9.
Luz expands log₂ (16/(x + 3)) on a math club card. Which choice is equal to it?
- 4 − log₂ x − log₂ 3
- log₂ (x + 3) − 4
- 4 − log₂ (x + 3)
- 4 ÷ log₂ (x + 3)
10.
Noah writes 3 log₂ x − log₂ 4 as one log on the class board. Which choice is it?
- log₂ (3x/4)
- log₂ (x³ − 4)
- log₂ (x³/4)
- log₂ (4/x³)

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

See all Algebra 2

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