Solve logarithmic equations

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Pia joins the logs to solve log₅ x + log₅ 8 − log₅ 2 = 2. What is x?

   25/4
2. 2.

   Ren joins the logs to solve log₂ x + 2 log₂ 3 = 5. What is x?

   32/9
3. 3.

   Tala joins the logs to solve log₃ x + 2 log₃ 5 = 4. What is x?

   81/25
4. 4.

   Zee solves ln x = 2.5 with a calculator. To the nearest hundredth, what is x?

   12.18
5. 5.

   Esme solves ln (2x) = 4 with a calculator. To the nearest hundredth, what is x?

   27.3
6. 6.

   Jun solves log (x − 3) = 1.5 with a calculator. To the nearest hundredth, what is x?

   34.62
7. 7.

   Luz solves log₂ (x² + 12) − log₂ x = 3 on a math club card. Which choice gives every solution?

   • x = 6 only
   • no solution
   • x = 2 only
   • x = 2 and x = 6
8. 8.

   Milo solves log₂ (x + 3) + log₂ (x − 3) = 4 on a math club card. Which choice gives every solution?

   • no solution
   • x = -5 only
   • x = 5 only
   • x = 5 and x = -5
9. 9.

   Noah solves log₃ (x² + 18) − log₃ x = 2 on a math club card. Which choice gives every solution?

   • x = 3 and x = 6
   • no solution
   • x = 3 only
   • x = 6 only
10. 10.

    Pia solves log₂ (x − 1) − log₂ (x + 3) = 1 on a math club card. Which choice gives every solution?

    • no solution
    • x = 7 only
    • x = -7 only