Curriculum / Math / 11th Grade / Unit 5: Exponential Modeling and Logarithms / Lesson 12
Math
Unit 5
11th Grade
Lesson 12 of 16
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Develop and use the product and quotient properties of logarithms to write equivalent expressions.
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
Allison says that:
$${\mathrm{log}1000}$$
$${=\mathrm{log}\left(10\cdot{100}\right)}$$
$${=\mathrm{log}10+\mathrm{log}100}$$
Show how Allison's reasoning is correct.
$${log 100}$$
$${=log\left(1000\over{10}\right)}$$
$${=log1000-log10}$$
Below are two graphs of logarithmic functions.
$${f(x)=\mathrm{log}_2x}$$
$${g(x)=\mathrm{log}_2(4x)}$$
What transformation occured? How can you use the rule you developed in the last problem to explain the transformation?
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
$${{\mathrm{log}_312}}$$
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 11
Lesson 13
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 power property 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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