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Exponential and Logarithmic Functions — High School Algebra 2 practice questions

18 multiple-choice questions and 21 flashcards on Exponential and Logarithmic Functions, about 12% of the High School Algebra 2 bank. Every one carries a written rationale.

Written and maintained by the CoStudy team · last updated 2026-10-12 · how we write and review questions

What this chapter covers

Exponential and Logarithmic Functions is one of 9 chapters in CoStudy's High School Algebra 2 bank, and it holds 18 of the bank's 150 multiple-choice questions — roughly 12% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.

Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.

Free Exponential and Logarithmic Functions practice questions

7 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.

$1,000 is invested at 5% interest, compounded yearly. What is it worth after 3 years?

  1. $1,157.63
  2. $1,150.00
  3. $1,050.00
  4. $1,500.00

Answer: A — $1,157.63

A) Correct — 1000(1.05)³. B) Uses simple interest. C) Uses one year only. D) Uses 50% instead of 5%.

Evaluate log₂(8).

  1. 4
  2. 3
  3. 16
  4. 6

Answer: B — 3

B) Correct — 2³ = 8. A) Divides 8 by 2. C) Multiplies 8 by 2. D) Subtracts 2 from 8.

Using the change-of-base formula, log₃(7) equals:

  1. log 3 / log 7
  2. log 7 − log 3
  3. log 7 / log 3
  4. log 7 · log 3

Answer: C — log 7 / log 3

C) Correct — log_b(a) = log a / log b. A) Inverts the ratio. B) Is log(7/3). D) Multiplies the logs.

Evaluate ln(e³).

  1. e³
  2. 3
  3. 1/3
  4. 3e

Answer: B — 3

B) Correct — ln and eˣ are inverses. A) Doesn't apply the logarithm. C) Inverts the exponent. D) Multiplies instead.

Solve log₂(x) + log₂(x − 2) = 3.

  1. x = 4
  2. x = 4 or x = −2
  3. x = −2
  4. x = 5

Answer: A — x = 4

A) Correct — x(x − 2) = 8 gives x = 4 or −2; logs need x > 2. B) Keeps the extraneous solution. C) Keeps only the extraneous solution. D) Solves x + x − 2 = 8.

log(a/b) equals:

  1. log a − log b
  2. log a / log b
  3. log(a − b)
  4. log a + log b

Answer: A — log a − log b

A) Correct — The quotient rule for logarithms. B) Divides the logs. C) Confuses the log of a difference with a difference of logs. D) Is the product rule.

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

  1. x > 2
  2. x ≥ 2
  3. x < 2
  4. All real numbers

Answer: A — x > 2

A) Correct — The argument of a log must be positive. B) Includes x = 2, where the argument is 0. C) Reverses the inequality. D) Ignores the restriction.

Exponential and Logarithmic Functions flashcards

4 cards from the 21 in this chapter.

What's 'continuously compounded' interest formula?

A = Pe^(rt). e ≈ 2.71828.

What is log₂(8)?

3. (2³ = 8.)

For y = 3 × 2ˣ, what's the y-intercept?

3 (when x = 0, y = 3 × 1 = 3).

Log property: log(ab) = ?

log(a) + log(b).

Practise the full chapter

These are a sample. The full Exponential and Logarithmic Functions chapter runs 39 items with per-chapter progress tracking, on the web and in the iOS app.

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