Solving Exponential Equations with Logarithms Practice Set
A practice set of eight problems, including one real-world population application, that has students solve exponential equations by taking logarithms and rounding answers to three decimal places. It builds fluency with isolating exponential terms and applying the inverse relationship between exponentials and logarithms, and it fits a single class period or homework assignment for 11th grade and above.
Teacher Guide & Tips
- Use this as guided practice after students have learned to take logarithms of both sides of an equation, ideally in a 45-minute block or as independent homework.
- Discussion question: Why do we isolate the exponential term before taking a logarithm, and what goes wrong if we try to take the log of a sum like 2·5^x + 8?
- Scaffold for struggling students: Have them work problems 1 through 4 first, where only one isolation step is needed, and model writing the log of both sides with a worked example beside the page.
- Extension for advanced students: Ask them to solve problem 8 in general form, finding the time t for any target population, and to explain what the answer means in context.
- Estimated time: about 25 to 35 minutes for all eight problems, depending on how much step-by-step work students show.
Solving Exponential Equations with Logarithms Practice Set
A practice set of eight problems, including one real-world population application, that has students solve exponential equations by taking logarithms and rounding answers to three decimal places. It builds fluency with isolating exponential terms and applying the inverse relationship between exponentials and logarithms, and it fits a single class period or homework assignment for 11th grade and above.
Teacher Guide & Tips
- Use this as guided practice after students have learned to take logarithms of both sides of an equation, ideally in a 45-minute block or as independent homework.
- Discussion question: Why do we isolate the exponential term before taking a logarithm, and what goes wrong if we try to take the log of a sum like 2·5^x + 8?
- Scaffold for struggling students: Have them work problems 1 through 4 first, where only one isolation step is needed, and model writing the log of both sides with a worked example beside the page.
- Extension for advanced students: Ask them to solve problem 8 in general form, finding the time t for any target population, and to explain what the answer means in context.
- Estimated time: about 25 to 35 minutes for all eight problems, depending on how much step-by-step work students show.