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Grade 11 · Math · Algebra 2

11th grade Solve logarithmic equations worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

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Solve logarithmic equations

Grade 11 Math Worksheet - Building Confidence

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

  1. Milo solves log₂ x = 7 on the class board. What is x?

  2. Noah solves log₇ x = 4 in a math book. What is x?

  3. Pia solves log₅ x = 4 on a math club card. What is x?

  4. Ren solves log₉ x = 3 on the class board. What is x?

  5. Tala solves log₃ (2x + 1) = log₃ 15 in a math book. What is x?

  6. Esme solves log₇ (5x − 4) = log₇ 26 in a math book. What is x?

  7. Jun solves log₂ x + log₂ (x − 2) = 3 and gets x = 4 or x = -2 before checking. Which choice gives every solution?

    • x = 4 and x = -2
    • x = -2 only
    • x = 4 only
    • no solution

  8. Kira solves log₂ (x² + 3) = log₂ (4x) and gets x = 1 or x = 3 before checking. Which choice gives every solution?

    • x = 1 and x = 3
    • x = 3 only
    • no solution, both answers fail
    • x = 1 only

  9. Luz solves log₃ x + log₃ (x − 2) = 1 and gets x = 3 or x = -1 before checking. Which choice gives every solution?

    • x = 3 only
    • no solution
    • x = -1 only
    • x = 3 and x = -1

  10. Milo solves log₃ (x² + 6) = log₃ (5x) and gets x = 2 or x = 3 before checking. Which choice gives every solution?

    • no solution
    • x = 3 only
    • x = 2 only
    • x = 2 and x = 3
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11th grade Solve logarithmic equations worksheet – printable
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About this worksheet

Logarithmic equations. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can rewrite log_b X = c as X = b^c and solve for x.
  • I can join logs with one base into one log, or set two insides equal, and solve.
  • I can check every answer in the first equation and keep only the ones whose insides are above 0.

Standard: A-REI.A.1 (related)

Words to know

logarithmic equation: An equation with x inside a log.

rewrite: Turn log_b X = c into X = b^c: X sits in row c.

inside (argument): The number or expression a log is taken of; it must be above 0.

condense: Join several logs with one base into one log.

fake answer (extraneous): An answer of the equation without logs that fails in the first equation.

check: Put the answer back into every log and make sure each inside is above 0.

Common mistakes

Rewrote log₂ x = 5 as x = 5² instead of x = 2⁵. Read it aloud together: "2 to the 5th power is x."

Multiplied the base by the number (2 × 5) instead of raising it (2⁵). Write 2⁵ as 2 × 2 × 2 × 2 × 2 together.

Moved a number across the equals sign with the wrong sign.

What to say

Ask: to undo + 3, do you add or subtract 3?

Questions parents ask

What is the most common mistake with solve logarithmic equations?

Rewrote log₂ x = 5 as x = 5² instead of x = 2⁵. Read it aloud together: "2 to the 5th power is x."

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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