Exponential equations: rewrite with the same base

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

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

   5
2. 2.

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

   7
3. 3.

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

   7
4. 4.

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

   4
5. 5.

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

   4
6. 6.

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

   5
7. 7.

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

   3/4
8. 8.

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

   -7/6
9. 9.

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

   5/6
10. 10.

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

    7/6