Week 14 — Readings & Resources · Logarithmic Functions

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective covered: Objective 8 — Analyze and apply exponential and logarithmic functions and equations.

How to use this page

Everything here is a link to an external resource — open it in your browser, the same way you'd open a YouTube link. Nothing needs to be downloaded.

This week's load is deliberately light: ~3 readings + ~2 videos, grouped by the four ideas from the lecture. Read or watch one item per group and you're ready for the quiz; do all of them and you'll be very comfortable. Total time is roughly 45–65 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① logs as inverses (evaluating) → ② graphs and domain → ③ properties (expand and condense).

A habit to reinforce this week: the AI tutorial has you catch a chatbot claiming log(x + 4) = log(x) + log(4). Keep that posture as you read — the tool drafts, you check.

① Logarithms as Inverses — Evaluating Logs & Converting Forms

Maps to Lecture Segments 1–2. The inverse definition, the "magic swap," mental evaluation, common log and natural log.

Reading — "Logarithmic Functions" (OpenStax, College Algebra 2e, §6.3)
🔗 https://openstax.org/books/college-algebra-2e/pages/6-3-logarithmic-functions
Why it's assigned: walks through the definition log_b(x)=y ↔ bʸ=x, converting between exponential and log form, evaluating logs mentally, and both the common log (base 10) and the natural log (base e). The Richter-scale example from the lecture hook is in this section.
⏱ ~12 min

② Graphs of Logarithmic Functions — Domain and Vertical Asymptote

Maps to Lecture Segment 3. Domain (argument > 0), vertical asymptote, graph shape, transformations.

Reading — "Graphs of Logarithmic Functions" (OpenStax, College Algebra 2e, §6.4)
🔗 https://openstax.org/books/college-algebra-2e/pages/6-4-graphs-of-logarithmic-functions
Why it's assigned: covers the domain rule (argument > 0), the vertical asymptote, and how horizontal/vertical shifts move the graph — exactly what the domain problems on the quiz test. If you have time for only one reading, combine this with §6.3 above.
⏱ ~10 min

Video — "Introduction to Logarithms and Their Graphs (Precalculus - College Algebra 55)" (Professor Leonard)
🔗 https://www.youtube.com/watch?v=jfnTwz79PWU
Why it earns the click: full whiteboard walkthrough of the inverse relationship and graph features — ideal if you want to see the conversion and the domain logic worked out slowly and carefully. Skim to the domain/graph section if you're short on time.
⏱ longer lecture (skim to the parts you need)

③ Properties of Logarithms — Expand and Condense

Maps to Lecture Segments 5–6. Product rule, quotient rule, power rule, expanding, condensing.

Reading — "Logarithmic Properties" (OpenStax, College Algebra 2e, §6.5)
🔗 https://openstax.org/books/college-algebra-2e/pages/6-5-logarithmic-properties
Why it's assigned: lays out all three properties with worked examples of expanding and condensing — the exact skills tested on the assignment. The pH chemistry example connects to the Discussion 14 prompt.
⏱ ~12 min

Reading — "Logarithm Functions" (Paul's Online Math Notes — Algebra)
🔗 https://tutorial.math.lamar.edu/classes/alg/LogFunctions.aspx
Why it's assigned: tight, example-driven reference page covering evaluation, the inverse relationship, and properties. Particularly good for seeing why log(M + N) ≠ log M + log N with a clear explanation. A strong second pass or quick-reference page.
⏱ ~8 min

Optional one-stop references (free online)

The same references from Week 13 cover Week 14's material:
🔗 Paul's Algebra notes (full log section): https://tutorial.math.lamar.edu/classes/alg/alg.aspx
🔗 Professor Leonard — College Algebra / Trigonometry playlist: https://m.youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP

Pick-one quick path (≈20 min total)

In a hurry? Do exactly these and you'll be ready for the quiz:
1. Read OpenStax §6.3 — Logarithmic Functions (group ①).
2. Read OpenStax §6.5 — Logarithmic Properties (group ③).
3. Watch Professor Leonard — Introduction to Logarithms (group ②) — fast-forward to the domain section.

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell Prof. Calloway and use the Paul's Online Math Notes reference above in the meantime.