Curriculum / Math / 11th Grade / Unit 5: Exponential Modeling and Logarithms / Lesson 13
Math
Unit 5
11th Grade
Lesson 13 of 16
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Develop and use the power property of logarithms to write equivalent expressions.
The core standards covered in this lesson
F.BF.B.4.B — Verify by composition that one function is the inverse of another.
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
Each logarithm below is written two ways. Evaluate each logarithm and identify any patterns in the table.
Algebra II > Module 3 > Topic B > Lesson 10 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Below is a statement:
$${\mathrm{log}_42={1\over2}\mathrm{log}_44}$$
Is this true? How do you know?
Show that $${y=\mathrm{ln}e^x}$$ is equivalent to $${y=x}$$.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Establish the property $${\mathrm{log}\left(1\over x\right)=-\mathrm{log}(x)}$$ for all $${x>0}$$ using the properties you have learned thus far.
Algebra II > Module 3 > Topic B > Lesson 12 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Write each logarithm as an equivalent expression involving only logarithms base 10.
a. $${\mathrm{log}_3(25)}$$
b. $${\mathrm{log}_{100}(x^2)}$$
Algebra II > Module 3 > Topic B > Lesson 13 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Rewrite each expression as an equivalent expression containing only one logarithm.
a. $${3\mathrm{ln}(p+q)- 2\mathrm{ln}(q) - 7\mathrm{ln}(p)}$$
b. $${\mathrm{ln}(xy)-\mathrm{ln}\left({x\over y}\right)}$$
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.
Lesson 12
Lesson 14
Topic A: Modeling with and Interpreting Exponential Functions
Identify, model, and analyze geometric sequences.
F.IF.A.3 F.IF.B.5 F.LE.A.2
Analyze and construct exponential functions that model contexts.
F.IF.B.4 F.IF.C.8.B F.LE.A.2
Write and change the form of exponential functions that model compounding interest.
F.BF.A.1.A F.LE.B.5
Define and use $$e$$ in continuous compounding situations.
A.SSE.B.3.C F.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.3 F.BF.B.4.B F.BF.B.4.C F.BF.B.5 F.IF.C.7.E
Evaluate common and natural logs using tables, graphs, and calculators.
F.BF.B.4.C F.LE.A.4
Understand and apply the change of base property to evaluate logarithms.
Develop and use the product and quotient properties of logarithms to write equivalent expressions.
F.BF.B.4.B F.LE.A.4
Solve equations with logarithms.
Use logarithms to solve exponential modeling problems (Part I).
A.SSE.A.1.B F.LE.A.4
Use logarithms to solve exponential modeling problems (Part II).
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