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

    x =

  2. Question 2

    Solve 3^(x − 3) = 27.

    x =

  3. Question 3

    Solve 9^(x + 2) = 3^x.

    x =

  4. Question 4

    Solve 8^x = 16. Give a fraction or decimal.

    x =

  5. Question 5

    Solve 3^x = 81.

    x =

  6. Question 6

    Solve 9^(x − 1) = 3^x.

    x =

  7. Question 7

    Solve 16^x = 8. Give a fraction or decimal.

    x =

  8. Question 8

    Solve 2^x = 16.

    x =

  9. Question 9

    Solve 9^(x + 4) = 3^x.

    x =

  10. Question 10

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

    x =

  11. Question 11

    Solve 3^(x − 1) = 81.

    x =

  12. Question 12

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

    x =

  13. Question 13

    Solve 16^x = 8. Give a fraction or decimal.

    x =

  14. Question 14

    Solve 5^(x − 3) = 125.

    x =

  15. Question 15

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

    x =

  16. Question 16

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

    x =

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  1. x = 1.5
  2. x = 6
  3. x = -4
  4. x = 1.33333333333
  5. x = 4
  6. x = 2
  7. x = 0.75
  8. x = 4
  9. x = -8
  10. x = 0.666666666667
  11. x = 5
  12. x = -3
  13. x = 0.75
  14. x = 6
  15. x = 1
  16. x = 1.5