Grade 11 · Math · Algebra 2

11th grade Exponential form and logarithmic form, evaluating logarithms, and change of base worksheet

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Exponential form and logarithmic form, evaluating logarithms, and change of base

Grade 11 Math Worksheet

NameDate

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

Bo solves a math club card that asks for log₂ (1/8). What is log₂ (1/8)?
Esme reads log 0.01 in a science book. What is log 0.01?
Jun writes log₉ 3 on the class board. What is log₉ 3?
4.
Kira writes log₂ (1/16) = -4 on a math club card. Which choice writes log₂ (1/16) = -4 as a power?
- 2^(1/16) = -4
- (-4)² = 1/16
- 2⁻⁴ = 1/16
- (1/16)⁻⁴ = 2
5.
Milo writes log 0.001 = -3 on the class board. Which choice writes log 0.001 = -3 as a power?
- (-3)¹⁰ = 0.001
- 0.001⁻³ = 10
- 10⁻³ = 0.001
- 10^(0.001) = -3
Read this first
Growth table, × 2 on each arrow
Row 0: 1; row 1: 2; row 2: 4; row 3: 8; row 4: 16; row 5: 32; row 6: 64.
6.
Noah looks for 20 in the × 2 growth table. log₂ 20 is between which two whole numbers?
- 4 and 5
- 3 and 4
- 5 and 6
- 1 and 2
7.
Row 0: 1; row 1: 5; row 2: 25; row 3: 125; row 4: 625. Ren looks for 300 in the × 5 growth table. log₅ 300 is between which two whole numbers?
- 2 and 3
- 4 and 5
- 3 and 4
- 5 and 6
Tala finds log₃ 50 with a calculator, using log₃ 50 = log 50 ÷ log 3. To the nearest hundredth, what is log₃ 50?
Zee finds log₇ 200 with a calculator, using log₇ 200 = log 200 ÷ log 7. To the nearest hundredth, what is log₇ 200?
Bo finds log₆ 90 with a calculator, using log₆ 90 = log 90 ÷ log 6. To the nearest hundredth, what is log₆ 90?

11th grade Exponential form and logarithmic form, evaluating logarithms, and change of base worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Logarithms: exponential and log form, values, and change of base. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can switch between 2⁵ = 32 and log₂ 32 = 5, and find a log by counting the arrows of a growth table.
I can find logs of numbers below 1, say which two whole numbers a log is between, and use ln for base e.
I can find any log on a calculator with log y ÷ log b, to the place asked.

Standard: F-BF.B.5 (+), F-LE.A.4

Words to know

logarithm: log_b y: the power of b that gives y; the row of the × b table.

base: The number multiplied on every arrow: the 2 in log₂ 32.

common log: log y with no base written: base 10.

natural log: ln y: the log with base e.

e: A number near 2.718, used as a base for growth.

change of base: log_b y = log y ÷ log b, for a calculator.

row: The step number in the growth table; row 0 holds 1.

Common mistakes

Divided the two numbers (32 ÷ 2) instead of counting how many times the base multiplies.

Counted the starting 1 as a step, so the answer came out one too big. Write 1, 2, 4, 8 and count the arrows between them together.

Mixed up the small base number and the big number inside the log. Read log₂ 8 aloud together as "2 to what power is 8?"

What to say

Ask: starting at 1, how many times do you multiply by 2 to reach 32?

Questions parents ask

What is the most common mistake with exponential form and logarithmic form, evaluating logarithms, and change of base?

Divided the two numbers (32 ÷ 2) instead of counting how many times the base multiplies.

How can I help my child with exponential form and logarithmic form, evaluating logarithms, and change of base?

Ask: starting at 1, how many times do you multiply by 2 to reach 32?

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.

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