Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Module: Week 14 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 8 — Analyze and apply exponential and logarithmic functions and equations.

This file holds two pieces: (A) the Module 14 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. Dates below assume a Tuesday/Thursday session pattern with Week 14 meeting Tue Dec 1 and Thu Dec 3, and end-of-week work due Sunday Dec 6, 11:59 p.m. Adjust the day-of-week and times to match your section.

Module start date: 2026-11-30 (Monday). No holiday falls in this week.

(A) Module 14 Overview — Start Here

Welcome to Week 14: Logarithmic Functions

This is your home base for the week. Read it first, then work the checklist below from top to bottom. Everything you need is linked inside the module.

Last week you mastered exponential functions — their graphs, growth, decay, and the natural base e. This week you meet exponential functions' mirror image: the logarithm. Every exponential fact has a logarithmic twin. Understanding that relationship is what unlocks solving exponential equations, modeling earthquakes, measuring sound, and reading pH labels — all things that show up in science, engineering, and everyday life.

The week's big question

"A logarithm is just an exponent in disguise — so why does that matter?"

By Sunday you'll convert fluently between exponential and logarithmic form, evaluate common and natural logs by hand, identify the domain and vertical asymptote of any log function, and apply the three properties of logarithms to expand or condense expressions.

By the end of this week, you can…

Use this as a checklist. If you can do all four, you're ready for the quiz.

• [ ] Define a logarithm as an inverse of an exponential — rewrite log_b(x)=y ⟺ bʸ=x in either direction and explain in plain language what the logarithm is asking.
• [ ] Evaluate logarithms mentally — log₂(8), log₁₀(1000), ln(e), log₅(1), and log₂(1/4) without a calculator, using the inverse definition.
• [ ] Identify the domain and vertical asymptote of a logarithmic function (argument must be > 0; VA where argument = 0) and connect these features to the log's graph.
• [ ] Apply the three properties of logarithms — product (log_b(MN) = log_b M + log_b N), quotient, and power (log_b(Mᵖ) = p·log_b M) — to expand and condense expressions.

What's due this week, and when

Work these in order — each one gets you ready for the next.

Heads-up on the AI tutorial: chatbots sometimes confuse log(M+N) with log M + log N (they're NOT equal) or try to take the log of a non-positive number. Catching those slips is part of the weekly AI-critique moment.

Late policy reminder: 10% off per day late. If life happens, reach out before the deadline — I'd much rather hear from you early.

How to succeed this week

• Say "log_b(x) asks: what power of b gives x?" out loud every time you see a logarithm. This one sentence decodes 90% of evaluation problems.
• The domain trap. The argument of any logarithm must be strictly greater than zero. When the argument is a variable expression like (x − 2), set it > 0 and solve — that's your domain. The vertical asymptote lives where the argument equals zero.
• The classic misconception. log(M + N) is NOT log M + log N. The product rule only applies to multiplication inside the argument. Write this on a sticky note.
• Two tools for checking. Desmos can graph the original and simplified expression side by side — identical graphs mean you expanded or condensed correctly. An approved chatbot can check your algebra, but verify its work; it sometimes invents a log property that doesn't exist.
• We're two weeks from the final. The log properties and evaluation techniques return on every remaining assessment. Invest the time this week.

(B) Welcome Announcement — Module 14

Release setting: post on the module's start day (offset = 0 days), i.e., Mon Nov 30, 2026 — not before. If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Mon Nov 30."

Subject: Week 14 — logarithms are just exponents in disguise 🔍

Hi everyone,

Quick riddle: "2 to what power gives you 8?" If you answered 3, you already know what log₂(8) means — it's 3. A logarithm is just that question written with different notation: log_b(x) asks what power of b gives you x.

This week — Logarithmic Functions — we flip the exponential story over. If Week 13 was about exponential functions and how fast things grow, Week 14 is about measuring that growth on a human scale. That's exactly what the Richter scale, the decibel scale, and the pH scale all do: they use logarithms to compress a staggering range of values into numbers we can actually compare.

Three things not to miss:
1. Lecture Tutorial 14 — work through log evaluation, domains, and the three properties with an approved chatbot and submit the share link. Due Sun Dec 6.
2. Quiz 14 (no AI on quizzes) closes Sun Dec 6 — ten items on evaluating logs, converting between exponential and log form, domain, and properties.
3. Assignment 14 — four AI-coached problems with a self-scored report, and Discussion 14 — an arguable question about why logarithmic scales are useful — both also close Sun Dec 6.

One thing to keep in mind as we head toward the finish line: the log properties you learn this week are the foundation for solving exponential equations in Week 15 and will definitely appear on the final. Solid work now pays compound interest.

Open the Start Here / Module Overview page first. See you Tuesday.

Prof. Calloway