Curriculum / Math / 11th Grade / Unit 5: Exponential Modeling and Logarithms / Lesson 8
Math
Unit 5
11th Grade
Lesson 8 of 16
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Describe and evaluate simple numeric logarithms (Part II).
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
N.RN.A.1 — Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5<sup>1/3</sup> to be the cube root of 5 because we want (5<sup>1/3</sup>)³ = 5(<sup>1/3</sup>)³ to hold, so (5<sup>1/3</sup>)³ must equal 5.
N.RN.A.2 — Rewrite expressions involving radicals and rational exponents using the properties of exponents.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson extends logarithms from whole numbers to fractions and negative numbers, and serves largely as practice to build fluency after being introduced to logarithms in the last lesson.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Using the integers 1 to 9, fill in the red and blue boxes so that the chart is accurate. You can only use a number once per red box and once per blue box.
Logs by is made available on Open Middle under the CC BY-NC-SA 4.0 license. Accessed Feb. 22, 2018, 4:40 p.m..
The graph below shows the function $${f(x)=4^x}$$
Find each value:
$${f(-1)}$$
$${f(-3)}$$
$${f\left ( 1\over2 \right )}$$
$${f\left ( 3\over2 \right )}$$
$${\mathrm{log}_4{1\over4}}$$
$${\mathrm{log}_4{1\over64}}$$
$${\mathrm{log}_42}$$
$${\mathrm{log}_48}$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Explain why $${\mathrm{log}_23>\mathrm{log}_32}$$.
Evaluate each log:
$${\mathrm{log}_927}$$
$${\mathrm{log}_{1\over10}1000d}$$
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 7
Lesson 9
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 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.
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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