Logarithm Properties and Base Change
Free to teach as-is — the teacher guide, student handout, and slides are included.
Free — we'll email you an access link. Google Docs format.
Objective
I can use the properties of logarithms to rewrite expressions and apply the change of base formula to evaluate logarithms including natural logs. I can find exact values for logs without calculators
Part 1 of 4
Warm-up video
Professor Dave Explains · 7:06Vetted channel
We don't generate video — this one is by Professor Dave Explains on YouTube. The practice questions and exit ticket below were drafted by AI for this objective, and every question is editable in the teacher guide.
Part 2 of 4
Key concepts
3 concepts
- 1
If the base of the log and the number that the log operates on are the same, the result will be one, because anything to the first power equals itself, but if we are taking the log of one, the result will always be zero, regardless of the base.
- 2
Logarithms are essentially exponents, so log of AB equals log of A plus log of B, and log of A/B equals log of A minus log of B.
- 3
The three ways to expand logarithmic expressions are the product rule, the quotient rule, and the power rule.
Part 3 of 4
Practice
3 questions
Using the properties of logarithms, expand the expression: log(5x² / y)
Condense the following expression into a single logarithm: 3log(x) + log(2) - log(y)
Part 4 of 4
Exit ticket
Quick comprehension check
“Simplify the expression: log₃(9x²) - log₃(x)”
Sample answer included in the free materials
Get the materials
Teacher guide, student handout, and slides — free, in Google Docs format
Teacher Guide
Complete lesson plan with answer keys and alternate activities
Student Handout
Printable worksheet
Slides
Ready to present
We'll ask for your email to send your access link — nothing else.
Teaching a group at a different level?
Where are your students right now? We'll rebuild this lesson to match — including the teacher guide, student handout, and slides, saved to your Google Drive.
Adapt This Lesson