Exponential equations: rewrite with the same base

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   Jun sees that both sides of 3^(2x + 1) = 3⁹ are powers of 3. What is x?

   4
2. 2.

   Luz sees that both sides of 10^(4x − 2) = 10¹⁰ are powers of 10. What is x?

   3
3. 3.

   Row 0: 1; row 1: 2; the rows go on. Milo solves 2^(x + 1) = 32 with the × 2 growth table. What is x?

   4
4. 4.

   Row 0: 1; row 1: 5; the rows go on. Pia solves 5^(x + 1) = 625 with the × 5 growth table. What is x?

   3
5. 5.

   Ren writes 4 and 32 as powers of 2 to solve 4^x = 32. What is x?

   5/2
6. 6.

   Tala writes 8 and 128 as powers of 2 to solve 8^x = 128. What is x?

   7/3
7. 7.

   Zee writes 27 and 243 as powers of 3 to solve 27^x = 243. What is x?

   5/3
8. 8.

   Bo solves 2^x = 1/16 on a math club card. What is x?

   -4
9. 9.

   Esme solves 3^x = 1/27 on a math club card. What is x?

   -3
10. 10.

    Jun solves 10^x = 0.001 on a math club card. What is x?

    -3