Week 15 — Exponential & Logarithmic Equations & Applications

Welcome to your Week 15 Start Here page.

Why this matters

Solving for an exponent tells a bank customer when savings double and a biology lab when a culture is ready.

In plain language

This week you solve for an unknown that sits up in an exponent. Some of these puzzles you can answer by writing both sides as powers of the same number. The rest need a logarithm (the exponent you need to turn a base into a given number), which brings the unknown down where you can reach it. You will also solve equations with the unknown inside a logarithm, and you will throw out any answer that asks for the logarithm of a negative number. Then you will answer the questions that make this topic worth learning: how long until money doubles, how long until it triples, and how long until a decaying sample is cut in half.

• Already covered: Week 1 set the exponent rules; Weeks 2 and 3 gave the substitution check and the domain; Weeks 11 and 12 named extraneous solutions; Weeks 13 and 14 built exponentials and logarithms.
• This week: exponential equations by matching bases and by taking logs, logarithmic equations with the domain check, and doubling time, tripling time, and half-life.
• How they connect: every solve this week uses a Week 14 conversion or property to undo a Week 13 exponential, and every answer ends with a Week 2 check.
• Where we're going next: Week 16 is the finals week. It brings no new material, only the cumulative final and its review bundle.

Focus

How do you get an unknown out of an exponent, and know the answer works?

By the end of this module, you should be able to:

• [ ] solve an exponential equation by matching bases or by taking a log
• [ ] solve a log equation and reject an extraneous candidate
• [ ] find a doubling time, a tripling time, and a half-life

To-do

Plan your week

1. Read Chapter 15 (about 50 minutes), then the lecture and slides.
2. Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
3. Do the Model/Build Studio (about 90 minutes), the discussion, and the assignment.
4. Take the quiz.

This week's checkpoint: solve 2ˣ = 10 exactly, and solve log(x) + log(x − 3) = 1 with the domain check.

You've got this

Go in order, and ask your instructor early if a step snags.

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