Curriculum / Math / 11th Grade / Unit 5: Exponential Modeling and Logarithms / Lesson 14
Math
Unit 5
11th Grade
Lesson 14 of 16
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Lesson Notes
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Solve equations with 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 foundational standards covered in this lesson
A.REI.A.1 — Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
A.SSE.A.2 — Use the structure of an expression to identify ways to rewrite it. For example, see x<sup>4</sup> — y<sup>4</sup> as (x²)² — (y²)², thus recognizing it as a difference of squares that can be factored as (x² — y²)(x² + y²).
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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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
Explain how you know that these two properties are true:
If $${b^x=b^y}$$, then $${{x=y}}$$ when $${b\neq 0}$$ and $${{b\neq 1}}$$.
If $${\mathrm{log}_bx=\mathrm{log}_by}$$, then $${{x=y}}$$ when $${b\neq0}$$ and $${{b\neq 1}}$$.
Solve $${5^x=5^{3x-4}}$$.
Solve.
$${\mathrm{log}_6(x+3)+\mathrm{log}_6(x-2)=1}$$
Take the natural log of both sides and solve.
$${e^{2x-1}=4e}$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Find all solutions to the following equations. Remember to check for extraneous solutions.
a. $${\mathrm{log}_2(3x+7)=4}$$
b. $${\mathrm{log}(x-1)+\mathrm{log}(x-4)=1}$$
Algebra II > Module 3 > Topic B > Lesson 14 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..
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.
Next
Use logarithms to solve exponential modeling problems (Part I).
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
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.
Develop and use the power property of logarithms to write equivalent expressions.
F.BF.B.4.BF.LE.A.4
A.SSE.A.1.BF.LE.A.4
Use logarithms to solve exponential modeling problems (Part II).
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