Unit 07 · 3 Weeks · 7 Lessons
Logarithmic Functions & Equations
How do logarithms reverse exponential processes, compress scale, and reveal time, magnitude, and rate?
Complete instructional sequence
Detailed Lessons
Lessons include objectives, formulas, concept development, worked examples, guided and independent practice, differentiated pathways, application, misconception analysis, mastery evidence, reflection, and local completion.
Logarithms as Inverses of Exponentials
A logarithm answers an exponent question. Domain requires x>0, and base requires b>0, b≠1.
Open detailed lesson
Lesson 02Common, Natural & Other Logarithmic Bases
Common and natural logarithms are standard tools, but any valid base may be used. Base choice reflects context or computational convenience.
Open detailed lesson
Lesson 03Product, Quotient & Power Properties
Logarithm properties come from exponent laws and apply only to valid positive arguments. They expand products and powers or condense sums and differences.
Open detailed lesson
Lesson 04Solving Exponential Equations with Logarithms
Logarithms solve exponential equations with unmatched bases. Keep exact log forms before approximating and interpret time or quantity units.
Open detailed lesson
Lesson 05Solving Logarithmic Equations & Domain Checks
Use log properties or convert to exponential form. Algebraic candidates may violate the domain, so substitution into the original is mandatory.
Open detailed lesson
Lesson 06Change of Base, Technology & Estimation
The change-of-base formula lets technology evaluate any valid logarithm and supports mental estimation by comparing nearby powers.
Open detailed lesson
Lesson 07Logarithmic Scales, Data & Model Interpretation
Log scales describe orders of magnitude, sound intensity, acidity, and other multiplicative phenomena. Differences on a log scale represent ratios in the original quantity.
Open detailed lesson
Practice and evidence
Unit Resources
Foundation Practice
Prerequisite support, smaller steps, representation aids, and correction prompts.
Core Practice
Complete standards-level definitive-answer practice and explanation.
Extended Practice
Generalization, proof, parameter analysis, technology, and deeper modelling.
Unit Mastery Check
Fresh randomized questions with scoring and explanations.
Logarithmic Scale & Inverse-Process Investigation
Applied investigation with evidence, validation, limitations, and defense.
Family Guide
Plain-language overview, support questions, and evidence expectations.
Teacher Guide
Pacing, differentiation, assessment, misconceptions, and records.
Vocabulary Data
Core English terms with Spanish, French, Arabic, and Portuguese support.
Standards Map
Unit concepts and broad national/international alignment categories.