Solve logarithmic equations

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   Milo solves log₂ x = 7 on the class board. What is x?

   128
2. 2.

   Noah solves log₇ x = 4 in a math book. What is x?

   2401
3. 3.

   Pia solves log₅ x = 4 on a math club card. What is x?

   625
4. 4.

   Ren solves log₉ x = 3 on the class board. What is x?

   729
5. 5.

   Tala solves log₃ (2x + 1) = log₃ 15 in a math book. What is x?

   7
6. 6.

   Zee solves log₅ (3x − 2) = log₅ 10 in a math book. What is x?

   4
7. 7.

   Bo solves log₂ (4x + 3) = log₂ 23 in a math book. What is x?

   5
8. 8.

   Jun solves log₂ x + log₂ (x − 2) = 3 and gets x = 4 or x = -2 before checking. Which choice gives every solution?

   • x = -2 only
   • x = 4 only
   • x = 4 and x = -2
   • no solution
9. 9.

   Kira solves log₂ (x² + 3) = log₂ (4x) and gets x = 1 or x = 3 before checking. Which choice gives every solution?

   • x = 1 and x = 3
   • x = 3 only
   • no solution, both answers fail
   • x = 1 only
10. 10.

    Milo solves log₃ (x² + 6) = log₃ (5x) and gets x = 2 or x = 3 before checking. Which choice gives every solution?

    • x = 3 only
    • x = 2 and x = 3
    • x = 2 only
    • no solution