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Solve exponential equations by matching bases

11th grade (Year 12 in England) · 16 questions · Common Core: HSA.REI.A.1, HSF.LE.A.4 · England: A-level Pure Mathematics

Name

Date

Score/ 16

  1. Question 1

    Solve 8^(x + 1) = 4^x.

    x =

  2. Question 2

    Solve 8^x = 4. Give a fraction or decimal.

    x =

  3. Question 3

    Solve 3^(x + 3) = 81.

    x =

  4. Question 4

    Solve 2^(x − 2) = 8^x.

    x =

  5. Question 5

    Solve 4^x = 8. Give a fraction or decimal.

    x =

  6. Question 6

    Solve 2^(x − 2) = 8.

    x =

  7. Question 7

    Solve 2^(x + 4) = 8^x.

    x =

  8. Question 8

    Solve 27^x = 9. Give a fraction or decimal.

    x =

  9. Question 9

    Solve 5^(x − 3) = 25.

    x =

  10. Question 10

    Solve 8^(x + 2) = 4^x.

    x =

  11. Question 11

    Solve 4^x = 8. Give a fraction or decimal.

    x =

  12. Question 12

    Solve 3^x = 27.

    x =

  13. Question 13

    Solve 3^(x − 4) = 9^x.

    x =

  14. Question 14

    Solve 25^x = 125. Give a fraction or decimal.

    x =

  15. Question 15

    Solve 3^(x + 2) = 27.

    x =

  16. Question 16

    Solve 9^(x + 1) = 3^x.

    x =

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Answer key: Solve exponential equations by matching bases

  1. 1. x = -3

  2. 2. x = 0.666666666667

  3. 3. x = 1

  4. 4. x = -1

  5. 5. x = 1.5

  6. 6. x = 5

  7. 7. x = 2

  8. 8. x = 0.666666666667

  9. 9. x = 5

  10. 10. x = -6

  11. 11. x = 1.5

  12. 12. x = 3

  13. 13. x = -4

  14. 14. x = 1.5

  15. 15. x = 1

  16. 16. x = -2