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 - Challenge Me

NameDate

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

Esme rewrites 8 and 32 as powers of 2 to find log₈ 32. What is log₈ 32?
Jun rewrites 27 and 9 as powers of 3 to find log₂₇ 9. What is log₂₇ 9?
Kira rewrites 4 and 1/32 as powers of 2 to find log₄ (1/32). What is log₄ (1/32)?
Luz rewrites 25 and 1/125 as powers of 5 to find log₂₅ (1/125). What is log₂₅ (1/125)?
Milo uses the ln key on a calculator to solve e^x = 15. To the nearest hundredth, what is x?
Noah uses the ln key on a calculator to solve e^x = 40. To the nearest hundredth, what is x?
Pia uses the ln key on a calculator to solve e^x = 0.5. To the nearest hundredth, what is x?
Tala finds log₄ 0.3 with a calculator, using log₄ 0.3 = log 0.3 ÷ log 4. To the nearest hundredth, what is log₄ 0.3?
Zee finds log₅ 0.02 with a calculator, using log₅ 0.02 = log 0.02 ÷ log 5. To the nearest hundredth, what is log₅ 0.02?
Esme finds log₉ 0.4 with a calculator, using log₉ 0.4 = log 0.4 ÷ log 9. To the nearest hundredth, what is log₉ 0.4?

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

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

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.

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?"

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

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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