Logs, Rewritten: Switching between Exponents and Logs

Logarithms, Explained

(So They Actually Make Sense)

Logarithms are often taught as a collection of rules to memorize.

That’s why students can follow steps in class — but freeze the moment the question changes.

This mini-lesson takes a different approach.

Instead of starting with formulas, it starts with meaning.

Students learn what a logarithm is asking before they are asked to manipulate it.

Through careful rewriting, visual structure, and deliberate pacing, logarithms become something students can reason through, not guess at.

What’s inside

• A structured, guided lesson explaining logarithms in clear, non-intimidating language
• Multiple worked examples that show how and why logarithmic expressions are rewritten
• A focus on switching between exponential and logarithmic form to solve equations
• Visual and structural cues to reduce common confusion about bases and exponents
• A summary that connects understanding to the standard logarithm rules
• A focused set of practice questions covering different log structures
• Full, clearly written solutions included at the end of the PDF

No tricks.

No memorized shortcuts without justification.

Just logic that holds together.

Who this is for

• Students who need structure before formulas
• Learners who’ve memorized log rules but don’t trust them
• Middle school and early high school students beginning logarithms
• Review, intervention, homework support, or small-group instruction
• Tutors and homeschoolers who want fewer blank stares and more “ohhh” moments

Approx. time: 20–30 minutes

11 pages.