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Exponential and Logarithmic Functions — High School Pre-Calculus practice questions

16 multiple-choice questions and 20 flashcards on Exponential and Logarithmic Functions, about 11% of the High School Pre-Calculus bank. Every one carries a written rationale.

Written and maintained by the CoStudy team · last updated 2026-10-02 · how we write and review questions

What this chapter covers

Exponential and Logarithmic Functions is one of 10 chapters in CoStudy's High School Pre-Calculus bank, and it holds 16 of the bank's 150 multiple-choice questions — roughly 11% 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

2 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.

Solve log₃ x = 4.

  1. x = 12
  2. x = 64
  3. x = 7
  4. x = 81

Answer: D — x = 81

D) Correct — Rewrite as 3⁴ = x. A) Multiplies the base by the exponent. B) Computes 4³ instead of 3⁴. C) Adds the base and the exponent.

What is the inverse of f(x) = eˣ?

  1. 1/eˣ
  2. ln x
  3. e^(−x)
  4. log₁₀ x

Answer: B — ln x

B) Correct — ln and eˣ undo each other. A) Is the reciprocal, not the inverse. C) Is the reflection across the y-axis. D) Uses the wrong base.

Exponential and Logarithmic Functions flashcards

4 cards from the 20 in this chapter.

State the product rule of logs.

log_b(MN) = log_b M + log_b N.

Evaluate log_2(8).

3, since 2³ = 8.

What is an exponential function f(x) = aᵇˣ's graph?

Smooth curve through (0, a). For b > 1, increasing; for 0 < b < 1, decreasing.

Solve: 2ˣ = 16.

x = 4.

Practise the full chapter

These are a sample. The full Exponential and Logarithmic Functions chapter runs 36 items with per-chapter progress tracking, on the web and in the iOS app.

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