Curriculum / Math / 11th Grade / Unit 5: Exponential Modeling and Logarithms / Lesson 10
Math
Unit 5
11th Grade
Lesson 10 of 16
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Evaluate common and natural logs using tables, graphs, and calculators.
The core standards covered in this lesson
F.BF.B.4.C — Read values of an inverse function from a graph or a table, given that the function has an inverse.
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
Given: $${f(x)=e^x}$$ and $${g(x)=10^x}$$
Use your calculator to write a table of values for $${f^{-1}(x)}$$ and $${g^{-1}(x)}$$.
Match the equivalent equations with the tables of values above.
Which graph below represents $${\mathrm{log}_{10}x}$$ and which represents $${\mathrm{log}_ex}$$?
The “Common Log” is a log with a base of $${10}$$. This is written as $${\mathrm{log}(x)}$$. The “Natural Log” is a log with a base of $$e$$. This is written as $${\mathrm{ln}(x)}$$.
Write each of the following exponential equations as either a common log or the natural log.
$${10}^x=y$$
$$e^x=y$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Joseph evaluated $${\mathrm{log}_232}$$ in his calculator and got $${1.505}$$. Why does his answer not make sense? How did he “plug in” the value in the calculator?
Lesson 9
Lesson 11
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
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.
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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