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.

   Milo solves 125^x = 25 in a math book. What is x?

   2/3
2. 2.

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

   1/2
3. 3.

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

   3/4
4. 4.

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

   1/6
5. 5.

   Bo solves 25^x = 1/√5 in a math book. What is x?

   -1/4
6. 6.

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

   -2/9
7. 7.

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

   • 2^(5x) = 3⁵
   • 5^(x + 2) = 5³
   • 5^(2x) = 5⁴
   • 5^(2x) = 5³
8. 8.

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

   • 2^(x + 4) = 2²
   • 2^(3x + 3) = 2³
   • 2^(3x + 3) = 2²
   • 2^(3x + 1) = 2²
9. 9.

   Luz rewrites 9^(x + 1) = 243 so both sides are powers of 3. Which equation is right?

   • 3^(2x + 2) = 3⁵
   • 3^(x + 3) = 3⁵
   • 3^(2x + 2) = 3⁶
   • 2^(3x + 3) = 5³
   • 3^(2x + 1) = 3⁵
10. 10.

    Milo rewrites 16^x = 8 so both sides are powers of 2. Which equation is right?

    • 2^(4x) = 2⁴
    • 2^(x + 4) = 2³
    • 2^(4x) = 2³