Curriculum / Math / 11th Grade / Unit 5: Exponential Modeling and Logarithms / Lesson 11
Math
Unit 5
11th Grade
Lesson 11 of 16
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Lesson Notes
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Understand and apply the change of base property to evaluate logarithms.
The core standards covered in this lesson
F.LE.A.4 — For exponential models, express as a logarithm the solution to ab<sup>ct</sup> = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Find the value of $${\mathrm{log}_316}$$.
Is the equation below true? How do you know?
$${\mathrm{log}_216={{\mathrm{log}16}\over{\mathrm{log}2}}}$$
$${\mathrm{log}_216={{\mathrm{ln}16}\over{\mathrm{ln}2}}}$$
What pattern do you see that you an extrapolate into a general rule?
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Show that $${\mathrm{log}_{100}x={{\mathrm{log}x}\over{2}}}$$.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
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Develop and use the product and quotient properties of logarithms to write equivalent expressions.
Topic A: Modeling with and Interpreting Exponential Functions
Identify, model, and analyze geometric sequences.
Standards
F.IF.A.3F.IF.B.5F.LE.A.2
Analyze and construct exponential functions that model contexts.
F.IF.B.4F.IF.C.8.BF.LE.A.2
Write and change the form of exponential functions that model compounding interest.
F.BF.A.1.AF.LE.B.5
Define and use $$e$$ in continuous compounding situations.
A.SSE.B.3.CF.BF.A.1.A
Describe the derivation of the formula for the sum of a finite geometric series and use it to solve problems.
A.SSE.B.4
Find the sum of an infinite geometric series.
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Topic B: Definition and Meaning of Logarithms
Describe and evaluate simple numeric logarithms (Part I).
F.LE.A.4
Describe and evaluate simple numeric logarithms (Part II).
Describe logarithms as the inverse of exponential functions and graph logarithmic functions.
F.BF.B.3F.BF.B.4.BF.BF.B.4.CF.BF.B.5F.IF.C.7.E
Evaluate common and natural logs using tables, graphs, and calculators.
F.BF.B.4.CF.LE.A.4
Develop and use the power property of logarithms to write equivalent expressions.
F.BF.B.4.BF.LE.A.4
Solve equations with logarithms.
Use logarithms to solve exponential modeling problems (Part I).
A.SSE.A.1.BF.LE.A.4
Use logarithms to solve exponential modeling problems (Part II).
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