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Grade 11 · Math · Algebra 2

11th grade Exponential equations: rewrite with the same base worksheet

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Exponential equations: rewrite with the same base

Grade 11 Math Worksheet - Challenge Me

NameDate

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

  1. Noah solves 4^(x + 1) = 8^(x − 1) on a math club card. What is x?

  2. Pia solves 9^(x − 1) = 27^(x − 3) on a math club card. What is x?

  3. Tala solves 8^(x + 1) = 16^(x − 1) on a math club card. What is x?

  4. Zee solves 3 · 2^(x + 1) = 96 on a math club card. What is x?

  5. Esme solves 2 · 5^(x − 1) = 250 on a math club card. What is x?

  6. Jun solves 4 · 10^(x − 3) = 400 on a math club card. What is x?

  7. Kira solves 4^(x − 1) = 1/√2 by writing both sides as powers of 2. What is x?

  8. Luz solves 9^(x + 1) = 1/∛3 by writing both sides as powers of 3. What is x?

  9. Milo solves 8^x = √32 by writing both sides as powers of 2. What is x?

  10. Noah solves 27^(x − 1) = √3 by writing both sides as powers of 3. What is x?

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11th grade Exponential equations: rewrite with the same base worksheet – printable
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About this worksheet

Exponential equations: rewrite both sides with the same base. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can solve 2^(x + 1) = 32 by finding the row of 32 in the × 2 table.
  • I can write both sides as powers of one base, like 9 = 3² and 27 = 3³, and then set the exponents equal.
  • I can handle fractions, roots and brackets in the exponent, and an x on both sides.

Standard: A-REI.A.1, F-LE.A.4 (related)

Words to know

exponential equation: An equation with x in an exponent, like 2^(x + 1) = 32.

same base: Both sides written as powers of one number, like 3^(2x) = 3³.

equate the exponents: Set the two exponents equal once the bases match.

power of a power: (3²)^x: the exponents multiply, giving 3^(2x).

negative exponent: A power below row 0: 2⁻⁴ = 1/16.

fraction exponent: A root as a power: √8 = 8^(1/2) = 2^(3/2).

Common mistakes

Divided the two numbers (27 ÷ 9) instead of writing both as powers of one base.

Found the right row but gave it as x, forgetting the number added to x in the exponent.

Moved a number across the equals sign without changing its sign. Solve x + 2 = 5 and x − 2 = 5 together and compare.

What to say

Ask: 9 is 3 to what power, and 27 is 3 to what power?

Ask: if x + 1 = 5, what is x?

Questions parents ask

What is the most common mistake with exponential equations: rewrite with the same base?

Divided the two numbers (27 ÷ 9) instead of writing both as powers of one base.

How can I help my child with exponential equations: rewrite with the same base?

Ask: 9 is 3 to what power, and 27 is 3 to what power?

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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