If you are citizen of an European Union member nation, you may not use this service unless you are at least 16 years old.
You already know Dokkio is an AI-powered assistant to organize & manage your digital files & messages. Very soon, Dokkio will support Outlook as well as One Drive. Check it out today!

A2-A-1-6

Page history last edited by Tashe Harris 6 years, 2 months ago

A2.A.1.6 Solve common and natural logarithmic equations using the properties of logarithms.

In a Nutshell

Students will apply the properties of logarithms, used for expanding and condensing logarithms, to solve logarithmic equations. They will check their results for extraneous solutions and understand why it is necessary that they check.

Student Actions	Teacher Actions
Students will learn efficient procedures and algorithms and develop procedural fluency for expanding and condensing logarithms according to the properties of logarithms. Students will develop accurate procedural fluency for solving logarithmic equations using the properties of logarithms while demonstrating flexible use of strategies and methods. Students will analyze the parts of a logarithmic equation, develop strategies for solving logarithmic equations and identify entry points to begin the search for a solution.They will find methods to verify their answers in context of a logarithmic equation and will always question the reasonableness of solutions and whether some of the solutions are extraneous. Students will develop a deep and flexible conceptual understanding of the inverse relationship between exponents and logarithms.	Anticipate what students might struggle with while learning procedures used to solve logarithmic equations and be prepared to support them productively through the struggle. Implement mathematical tasks that provide students opportunities to build fluency of procedures and algorithms for solving logarithmic equations using the properties of logarithms. Select tasks that provide multiple entry points for solving logarithmic equations. Pose purposeful questions that allow students to discuss and explain why some solutions are extraneous. Focus students’ attention on the structure or essential features, i.e. bases, of exponents and logarithms and how they are related.
Key Understandings	Misconceptions
Relate the properties of logarithms to the properties of exponents. Expand or condense logarithms according to the properties of logarithms. Take the antilog of each side of an equation after the logarithms have been condensed to a single logarithm. Check solutions for extraneous roots.	Procedural: Students do not condense logarithms to a single logarithm on one or both sides of an equation before taking the antilog of each side. Students don’t apply the properties of logarithms correctly. Conceptual: Students fail to check their solutions within the context of the original equation.