Home › Certifications › High School Algebra 2 › Exponential and Logarithmic Functions
20 multiple-choice questions and 17 flashcards on Exponential and Logarithmic Functions, about 13% of the High School Algebra 2 bank. Every one carries a written rationale.
Exponential and Logarithmic Functions is one of 9 chapters in CoStudy's High School Algebra 2 bank, and it holds 20 of the bank's 150 multiple-choice questions — roughly 13% 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.
5 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 5^(x + 1) = 125.
Answer: C — x = 2
A) Multiplied 5 × 5 instead of recognizing the exponent. B) Solved 5^x = 125 and forgot the +1 in the exponent. C) Express 125 as 5³, so 5^(x + 1) = 5³ → x + 1 = 3 → x = 2. D) Confused base and exponent.
What is log(a · b)?
Answer: B — log(a) + log(b) (product rule of logarithms)
Logarithm properties: log(ab) = log(a) + log(b) (product), log(a/b) = log(a) - log(b) (quotient), log(aⁿ) = n·log(a) (power). Foundation for solving log equations. Algebra 2 staple.
Solve log₂(x) + log₂(x − 2) = 3.
Answer: A — x = 4
Combine: log₂(x(x−2)) = 3 → x² − 2x = 8 → x² − 2x − 8 = 0 → (x − 4)(x + 2) = 0 → x = 4 or x = −2. Check domain: need x > 0 and x − 2 > 0, so x > 2. Only x = 4 valid. B) Kept extraneous. C) Picked extraneous. D) Arithmetic slip.
Which is the standard form of a quadratic function?
Answer: D — f(x) = ax² + bx + c (a ≠ 0)
Quadratic: degree 2 polynomial. Standard form ax² + bx + c. Vertex form a(x-h)² + k. Factored form a(x-r₁)(x-r₂). Each form useful for different purposes.
Convert log₂(8) to evaluate.
Answer: B — 3 (2³ = 8, so log₂(8) = 3)
Logarithm definition: log_b(x) = y means b^y = x. log₂(8): what power of 2 gives 8? 2³ = 8, so log₂(8) = 3. Foundation of logarithmic functions.
4 cards from the 17 in this chapter.
For y = 3 × 2ˣ, what's the y-intercept?
3 (when x = 0, y = 3 × 1 = 3).
What's an 'exponential function'?
y = aᵇˣ where a is initial value and b is the base. Models growth or decay.
What is log(1000)?
3. (Default base 10. 10³ = 1000.)
What is the 'natural log' (ln)?
Logarithm base e. ln(x) = log_e(x).
These are a sample. The full Exponential and Logarithmic Functions chapter runs 37 items with per-chapter progress tracking, on the web and in the iOS app.
Open High School Algebra 2 in CoStudy →