Grade 11 · Math · Algebra 2

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

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Exponential equations: rewrite with the same base

Grade 11 Math Worksheet - Building Confidence

NameDate

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

Kira sees that both sides of 2^(3x + 4) = 2¹⁹ are powers of 2. What is x?
Luz sees that both sides of 10^(4x − 2) = 10¹⁰ are powers of 10. What is x?
Row 0: 1; row 1: 2; the rows go on. Milo solves 2^(x + 1) = 32 with the × 2 growth table. What is x?
Row 0: 1; row 1: 3; the rows go on. Noah solves 3^(x − 1) = 243 with the × 3 growth table. What is x?
Row 0: 1; row 1: 5; the rows go on. Pia solves 5^(x + 1) = 625 with the × 5 growth table. What is x?
Ren writes 4 and 32 as powers of 2 to solve 4^x = 32. What is x?
Tala writes 8 and 128 as powers of 2 to solve 8^x = 128. What is x?
Zee writes 27 and 243 as powers of 3 to solve 27^x = 243. What is x?
Esme solves 3^x = 1/27 on a math club card. What is x?
Jun solves 10^x = 0.001 on a math club card. What is x?

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

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)

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).

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.

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

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

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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