Week 15 — Readings & Resources · Exponential & Logarithmic Equations & Applications

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective covered: Objective 8 — Analyze and apply exponential and logarithmic functions, including solving equations and modeling real-world growth, decay, and financial scenarios.

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: ~2 readings + ~2–3 videos, grouped by the week's three skill clusters. 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 40–55 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① solving exponential equations (same-base and log-of-both-sides) → ② solving logarithmic equations (condense, convert, check domain) → ③ applications (compound interest, doubling time, half-life, decay models).

A habit to carry into finals week: the AI tutorial this week ends with you catching a chatbot that fails to discard an extraneous log solution. Keep that posture for the final — the tool drafts, you check.

① Solving Exponential Equations

Maps to Lecture Segments 2–3. Two methods: match bases (same-base) or apply log/ln to both sides (log-of-both-sides).

Reading — "Exponential and Logarithmic Equations" (OpenStax, College Algebra 2e, §6.6)
🔗 https://openstax.org/books/college-algebra-2e/pages/6-6-exponential-and-logarithmic-equations
Why it's assigned: the week's primary text source — covers both the same-base method and the log-of-both-sides method with worked examples, including the power rule reminder and the exact vs. decimal-approximation distinction.
⏱ ~12 min (read through the exponential-equations section)

Video — "Solving Exponential Equations with Logarithms" (Professor Leonard — Precalculus / College Algebra 64)
🔗 https://www.youtube.com/watch?v=rDcLCA2W-UI
Why it earns the click: a comprehensive, board-worked lecture covering exactly how to apply logarithms to isolate variables in exponential equations — including cases with exponential terms on both sides. Ideal if you want to see every step before trying problems yourself.
⏱ full lecture (skim to the parts you need)

② Solving Logarithmic Equations (and Catching Extraneous Solutions)

Maps to Lecture Segment 4. Condense → convert → check domain — and never skip that last step.

Reading — "Exponential and Logarithmic Equations" (OpenStax, College Algebra 2e, §6.6 — scroll to the logarithmic-equations section)
🔗 https://openstax.org/books/college-algebra-2e/pages/6-6-exponential-and-logarithmic-equations
Why it's assigned: the same §6.6 page continues into logarithmic equations — product-rule condensing, converting to exponential form, and the all-important extraneous-solution check. The examples mirror our Week 15 lecture closely.
⏱ ~8 min (the logarithmic-equations portion)

Reading — "Solving Logarithm Equations" (Paul's Online Math Notes — Algebra)
🔗 https://tutorial.math.lamar.edu/classes/alg/SolveLogEqns.aspx
Why it's assigned: Paul's tight, step-by-step walkthrough puts the domain check front and center with examples that make clear why you can never skip it. A great complement to the OpenStax treatment and excellent pre-quiz review.
⏱ ~10 min

Video — "Solving Logarithmic Equations with Exponentials" (Professor Leonard — Precalculus / College Algebra 63)
🔗 https://www.youtube.com/watch?v=jNUyVClUQfc
Why it earns the click: a full board-worked session specifically on log equations — condensing, converting to exponential form, and identifying extraneous solutions — from the same Professor Leonard series.
⏱ full lecture (skim to the parts you need)

③ Applications — Compound Interest, Doubling Time, Half-Life

Maps to Lecture Segments 5–6. A = Pe^(rt) for continuous compounding; A = A₀·e^(−kt) for decay. Solve for t by taking ln.

Reading — "Exponential and Logarithmic Models" (OpenStax, College Algebra 2e, §6.7)
🔗 https://openstax.org/books/college-algebra-2e/pages/6-7-exponential-and-logarithmic-models
Why it's assigned: the application chapter — compound interest, Newton's Law of Cooling, logistic growth, and half-life — with the formula derivations and setup strategies. Focus on the compound-interest and exponential-decay sections.
⏱ ~12 min (interest + decay sections)

Reading — "Solving Exponential Equations" (Paul's Online Math Notes — Algebra)
🔗 https://tutorial.math.lamar.edu/classes/alg/SolveExpEqns.aspx
Why it's assigned: a clean, worked-examples-first page on exponential equations that includes application-style problems. Good for seeing how the setup step (writing the equation before solving) is treated in a slightly different voice.
⏱ ~8 min

Optional one-stop references (free online)

If you'd like one optional reference to return to, Paul's Online Math Notes — Algebra keeps a full, free set of notes, and Professor Leonard's College Algebra / Precalculus playlist has full-length lectures for every topic in this course.
🔗 Paul's Algebra notes: https://tutorial.math.lamar.edu/classes/alg/alg.aspx
🔗 Professor Leonard — College Algebra / Trigonometry playlist: https://m.youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP
Why they're here: excellent cumulative resources for final-exam review — entirely optional this week.

Pick-one quick path (≈20 min total)

In a hurry? Do exactly these and you'll be ready for the quiz:
1. Read OpenStax §6.6 — exponential and logarithmic equations sections (covers Methods 1 and 2 + the extraneous-solution check).
2. Read Paul's Online Notes — Solving Logarithm Equations (domain-check emphasis).
3. Skim OpenStax §6.7 — compound interest and exponential decay application setup.

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.