Prep36 › Guides › ACT Exponential & logarithmic practice questions

ACT Exponential & logarithmic practice questions

Exponential & logarithmic sits in the Functions reporting category on the ACT Math section. Prep36 has 11 questions tagged to this skill, every one with a worked explanation. Three of them are below in full, with the reasoning, so you can see what the skill actually looks like before you practise it.

On this page

What Exponential & logarithmic covers on the ACT

Within this skill the Prep36 bank covers exponential growth by doubling, logarithmic equation with extraneous root, solving for time from a growth factor, doubling time growth, solving logarithmic equations and doubling periods.

Math is 45 questions in 50 minutes, which is about 66 seconds each, and it is one of the three sections that average into your composite. The difficulty split across the 11 questions tagged here is 0 easier, 4 medium and 7 harder.

Questions are original, written to the Enhanced ACT format. Prep36 is not affiliated with ACT, Inc.

3 exponential & logarithmic questions, with the reasoning

Question 1 medium

A biology class begins an experiment with 500 bacteria in a dish. The population doubles every 3 hours. If the doubling pattern continues, how many bacteria will be in the dish after 12 hours?

  1. A. 2,000
  2. B. 4,000
  3. C. 8,000 correct
  4. D. 16,000
Why: Twelve hours divided by a 3-hour doubling period is 4 doublings, so the population is 500 × 24 = 500 × 16 = 8,000, choice C. The choice 4,000 counts only 3 doublings, the classic off-by-one. The choice 2,000 counts 2 doublings, and 16,000 counts 5. All three wrong choices use the right method with the wrong exponent. Tip: on doubling problems, list the checkpoints instead of trusting a formula: 0 hr = 500, 3 hr = 1,000, 6 hr = 2,000, 9 hr = 4,000, 12 hr = 8,000. Ten seconds of listing beats an exponent error.
Question 2 hard

What is the solution set of log3(x + 5) + log3(x - 3) = 2 ?

  1. A. x = -6 only
  2. B. x = 3.5 only
  3. C. x = 4 only correct
  4. D. x = -6 and x = 4
Why: Use the product rule to combine the logs: log3[(x + 5)(x - 3)] = 2, so (x + 5)(x - 3) = 32 = 9. Expanding gives x2 + 2x - 15 = 9, or x2 + 2x - 24 = 0, which factors as (x + 6)(x - 4) = 0 and yields x = -6 or x = 4. But x = -6 makes both log arguments negative, so it is extraneous and the solution set is x = 4 only. The choice listing both values is wrong for exactly that reason, and x = 3.5 does not satisfy the equation at all.Tip: solving a log equation always has a second half. Every candidate root must make every log argument strictly positive, so test each one before you answer.
Question 3 medium

A biologist starts with 400 bacteria in a dish. The number of bacteria doubles every 3 hours. How many bacteria are in the dish after 12 hours?

  1. A. 1,600
  2. B. 3,200
  3. C. 4,800
  4. D. 6,400 correct
Why: Twelve hours divided by a 3 hour doubling time gives 4 doubling periods, so the population is 400 · 2⁴ = 400 · 16 = 6,400. Choice A (1,600) multiplies 400 by 4, treating the growth as if it were linear rather than repeated doubling. Choice B (3,200) uses only 3 doublings, and choice C (4,800) is not a doubling result at all. Tip: for doubling problems, always find the number of periods first, then raise 2 to that power. Multiplying by the number of periods is the classic linear-versus-exponential mistake.

The explanation is the point. Getting a question wrong tells you nothing you did not already suspect; knowing which step you missed is what changes the next one.

Practise the rest of the 11

The other 8 questions on this skill are in the free question bank, filterable by difficulty, each with the same worked explanation. No account and no card.

Open the Math bank

Frequently asked questions

How many ACT exponential & logarithmic questions does Prep36 have?
11, each tagged to this skill and each with a worked explanation.
Are these real ACT questions?
No. They are original questions written to the Enhanced ACT format. Prep36 is not affiliated with ACT, Inc.
Is the Math section part of the composite?
Yes. On the Enhanced ACT the composite is the average of English, Math and Reading. Science is optional and reported separately.
Keep readingACT Math practiceEvery Math skill in one place.How many questions can you miss?The miss budget for every score.ACT Score CalculatorTurn raw scores into a composite.
FREE DOWNLOAD

You just read the rule. Here is the version you can keep.

The free Enhanced ACT Cram Kit puts it on one printable page per section, plus a pacing table and a test-day checklist. Your email unlocks the download.

We use your email to send the Cram Kit and occasional ACT prep tips. Unsubscribe anytime. We never sell it or share it.

The whole question bank is free

1,026 original questions and 2 full-length timed tests, free. Every answer explained. No paywall at question 11.

Go to Prep36