math · Grade 11
Algebra 2: Exponential & Logarithmic Functions
Evaluate logarithms, apply exponent rules, solve exponential decay and compound interest equations with step-by-step mathematical solutions.
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Learning goals
- Express logarithms as inverse functions of exponentials: log_b(y) = x if and only if b^x = y
- Apply the product, quotient, and power rules of logarithms to condense and expand algebraic expressions
- Model and solve exponential growth, radioactive half-life, and continuously compounded interest problems
Before you begin
Work with exponents and understand inverse operations.
Age and grade do not measure readiness. Adjust reading or adult support to preserve the intended learning goal.
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1. Practice
Practice previewAlgebra 2: Exponential & Logarithmic Functions
Practice · Independent · 15 min
Evaluate logarithms, apply exponent rules, solve exponential decay and compound interest equations with step-by-step mathematical solutions.
Teaching and response guide
- Model the target skill: express logarithms as inverse functions of exponentials: log_b(y) = x if and only if b^x = y. Use the first task as a guided example before asking for an independent response.
- Check readiness first: Work with exponents and understand inverse operations.
- Discuss an incorrect response using this distinction: A logarithm asks for an exponent; it is not the exponent's product with the base.
Watch for: A logarithm asks for an exponent; it is not the exponent's product with the base.
Check the answer criteria for each task. A supported explanation may have more than one acceptable response. These activities offer evidence to discuss; completing a sheet alone does not establish mastery.
Possible next goals
Choose the next unit when its prerequisites fit your learner.