Exponential equations: rewrite with the same base

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Luz solves 32^x = 8 on the class board. What is x?

   3/5
2. 2.

   Noah solves 9^(x − 1) = 27 by writing both sides as powers of 3. What is x?

   5/2
3. 3.

   Pia solves 4^(x + 3) = 32 by writing both sides as powers of 2. What is x?

   -1/2
4. 4.

   Ren solves 8^(x − 2) = 16 by writing both sides as powers of 2. What is x?

   10/3
5. 5.

   Tala solves 25^(x + 1) = 125 by writing both sides as powers of 5. What is x?

   1/2
6. 6.

   Zee solves 4^x = √8 on a math club card. What is x?

   3/4
7. 7.

   Ari solves 9^x = ∛3 on the class board. What is x?

   1/6
8. 8.

   Esme solves 8^x = 1/∛4 on a math club card. What is x?

   -2/9
9. 9.

   Jun rewrites 25^x = 125 so both sides are powers of 5. Which equation is right?

   • 5^(x + 2) = 5³
   • 5^(2x) = 5³
   • 5^(2x) = 5⁴
   • 2^(5x) = 3⁵
10. 10.

    Kira rewrites 8^(x + 1) = 4 so both sides are powers of 2. Which equation is right?

    • 2^(3x + 3) = 2²
    • 2^(3x + 1) = 2²
    • 2^(3x + 3) = 2³
    • 2^(x + 4) = 2²