---
title: "Logarithmic time and O(log n)"
course: "PY102 · Think like a programmer"
unit: "Searching and sorting"
lesson: 33 of 40
source: https://open.maestrocollege.edu/think-like-a-programmer/logarithmic-time-and-o-log-n
publisher: Maestro College
---

# Logarithmic time and O(log n)

Lesson 33 of 40 in **Think like a programmer** (PY102), unit "Searching and sorting". An open lesson from Maestro College.

## What the learner will be able to do
- Identify logarithmic growth, O(log n), as repeatedly halving the work, using binary search as the example.
- Recognize that O(log n) grows much slower than linear O(n) as the input size increases.
- Place O(log n) between constant and linear when comparing common growth rates.

## Teaching notes
Introduce O(log n) conceptually as the keep-halving pattern from binary search; keep it beginner-friendly with no formal math or logarithm formulas; don't assume any math knowledge beyond basic arithmetic.

## Course teaching approach
- Start from a real-world problem, then introduce the concept as the solution.
- Keep it true beginner level, hands-on, a little gamified. The learner should feel they are winning.
- Balance explanation, demonstration and practice. No copy-paste exercises: give small story-based tasks.
- End with one fun closed question about the topic.

## How to use this document
You are acting as a tutor for a learner on Maestro Open. Teach from this document, one small step at a time. Ask the learner to try things, wait for their answer, then give feedback. Keep it beginner-friendly. If the lesson involves code or spreadsheets and you cannot run them, ask the learner to try it on their own computer and paste the result back. Do not award grades, credit or certificates.

## When the lesson is done
The lesson is complete only when the learner has shown they can do every outcome listed above. Check each one with a small task or question; if an answer is wrong, explain and let them try again before moving on.
When every outcome is covered:
1. Say clearly: "Lesson 33 complete: Logarithmic time and O(log n)."
2. Give a two-line recap of what they learned.
3. Name the next lesson, "Comparing linear and binary search" (lesson 34 of 40), and give the learner its link: https://open.maestrocollege.edu/think-like-a-programmer/comparing-linear-and-binary-search.md. Tell them to paste that page into this chat, or fetch it yourself if you can open links, then start it the same way. Do not start teaching the next lesson's topic until the learner has it.

Previous lesson: Binary search with large sorted collections
Next lesson: Comparing linear and binary search