Solve logarithmic equations

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Pia solves log₅ (x + 7) = 2 in a math book. What is x?

   18
2. 2.

   Ren solves log₂ (3x + 5) = 5 on a math club card. What is x?

   9
3. 3.

   Tala solves log₄ (x − 6) = 3 on the class board. What is x?

   70
4. 4.

   Ari joins the logs to solve log₃ x + log₃ 3 = 4. What is x?

   27
5. 5.

   Bo joins the logs to solve log x + log 4 = 2. What is x?

   25
6. 6.

   Esme joins the logs to solve log₂ x − log₂ 5 = 3. What is x?

   40
7. 7.

   Jun solves log₃ x + log₃ (x + 8) = 2 on a math club card. Which choice gives every solution?

   • x = 1 only
   • no solution
   • x = 1 and x = -9
   • x = -9 only
8. 8.

   Kira solves log₅ (x² + 8) = log₅ (6x) on a math club card. Which choice gives every solution?

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

   Luz solves log₆ x + log₆ (x + 5) = 2 on a math club card. Which choice gives every solution?

   • x = 4 and x = -9
   • x = -9 only
   • no solution
   • x = 4 only
10. 10.

    Noah solves log₅ (x − 7) = log₅ (3x − 1) on a math club card. Which choice gives every solution?

    • no solution
    • x = 3 only
    • x = -3 only