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Math 30-1 · Worksheets

Exponents and logs · Set A

Ten questions of mixed difficulty, covering Exponents and logs. Print it, or work through it on screen — the answer key starts on its own page.

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Exponents and logs · Set A

Math 30-1 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. On the Richter scale, how many times more intense is a magnitude 7 earthquake than a magnitude 5?

    1. a) 2
    2. b) 1000
    3. c) 20
    4. d) 100

  2. What is the domain of y = log(x − 2)?

    1. a) all real numbers
    2. b) x > 2
    3. c) x > 0
    4. d) x > −2

  3. What is the horizontal asymptote of y = 2ˣ?

    1. a) y = 2
    2. b) y = 0
    3. c) x = 0
    4. d) y = 1

  4. Evaluate 2 log 5 + log 4.

    1. a) 10
    2. b) 100
    3. c) 2
    4. d) log 14

  5. If log 2 = a and log 3 = b, which expression equals log 12?

    1. a) 2ab
    2. b) 2a + b
    3. c) a + b
    4. d) a²b

  6. $1000 is invested at 6% interest, compounded annually. To the nearest tenth, how many years until it doubles?

    1. a) 11.9
    2. b) 16.7
    3. c) 33.3
    4. d) 12.5

  7. Evaluate log₂ 8.

    1. a) 3
    2. b) 2
    3. c) 4
    4. d) 16

  8. y = log₃ x is the inverse of which function?

    1. a) y = 3ˣ
    2. b) y = x/3
    3. c) y = x³
    4. d) y = 3x

  9. Evaluate log₃(1/9).

    1. a) 2
    2. b) −3
    3. c) −2
    4. d) 1/2

  10. Evaluate log₅ 1.

    1. a) 1
    2. b) undefined
    3. c) 0
    4. d) 5

Answer key · Exponents and logs · Set A

Math 30-1 · maddyhelps.com

  1. d) 100 — Each step up is 10 times more intense. Two steps is 10² = 100 times, not 2.
  2. b) x > 2 — You can only take the log of a positive number, so x − 2 > 0, meaning x > 2. The graph has a vertical asymptote at x = 2.
  3. b) y = 0 — As x gets very negative, 2ˣ shrinks toward 0 but never reaches it, so the graph hugs y = 0. y = 1 is the y-intercept.
  4. c) 2 — The power law moves the 2 inside: log 25 + log 4. The product law combines them: log 100 = 2.
  5. b) 2a + b — 12 = 2² × 3, so log 12 = log 2² + log 3 = 2a + b. Logs turn multiplying into adding and powers into multipliers.
  6. a) 11.9 — Set 2000 = 1000(1.06)ⁿ, so 2 = 1.06ⁿ and n = log 2 ÷ log 1.06 ≈ 11.9. 16.7 comes from 100 ÷ 6, which ignores compounding.
  7. a) 3 — A logarithm asks for an exponent: 2 to what power is 8? 2³ = 8, so the answer is 3.
  8. a) y = 3ˣ — A logarithm undoes an exponential with the same base, so log₃ x and 3ˣ are inverses — reflections of each other in y = x.
  9. c) −2 — 1/9 = 3⁻², so the exponent is −2. A fraction less than 1 always gives a negative log when the base is bigger than 1.
  10. c) 0 — Any base to the power 0 is 1, so log of 1 is always 0. It is log₅ 5 that equals 1.