← Back to the College Algebra outline The Course Maker
← College Algebra outline
Week 14 · Module overview

Week 14 — Logarithmic Functions

College Algebra Free sample edition

Welcome to your Week 14 Start Here page.

Why this matters

A logarithm counts how many times something was multiplied: a sound engineer reads one on a decibel meter, and a lab technician uses one to count the half-lives in a sample.

In plain language

This week you learn to ask a power for its exponent. Last week you fed an input into a growth rule and got an output; now you know the output and want the input back. A logarithm (the exponent you need to turn a base into a given number) answers that question. You will switch between a logarithm and the power it describes, work out logarithms in your head, and draw the graph of a logarithmic function (a rule whose output is a logarithm). Then you will use three rules that let you split one logarithm into simpler pieces or merge several into one, and you will learn the one move that has no rule at all.

  • Already covered: Week 1 set the exponent rules; Week 2 solved inequalities; Week 10 named the vertical asymptote; Week 13 built exponential functions.
  • This week: the logarithm as an exponent, the common and natural logs, the log graph and its domain, and the three log properties.
  • How they connect: a log runs a Week 13 exponential backwards, and each log property is a Week 1 exponent rule.
  • Where we're going next: Week 15, Exponential & Logarithmic Equations & Applications, uses these properties to solve for an unknown exponent.

Focus

How do you find the exponent you need, and which log rewrites are safe?

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

  • [ ] convert between log form and exponential form
  • [ ] evaluate logs from the powers of a base
  • [ ] find the domain and asymptote of a log function
  • [ ] expand and condense logs, and refuse to split a sum

To-do

Plan your week

  1. Read Chapter 14 (about 45 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: evaluate log₂(1⁄4) and explain why log₂(4 + 4) is not log₂(4) + log₂(4).

You've got this

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

Built with The Course Maker · samples.thecoursemaker.com