Exponential Modeling and Logarithms

Lesson 11

Math

Unit 5

11th Grade

Lesson 11 of 16

Objective


Understand and apply the change of base property to evaluate logarithms.

Common Core Standards


Core Standards

  • F.LE.A.4 — For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

Criteria for Success


  1. Explain why the change of base property helps to evaluate logarithms on a calculator.
  2. Apply the change of base property to evaluate logarithms.
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Anchor Problems


Problem 1

Find the value of $${\mathrm{log}_316}$$.

Guiding Questions

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Problem 2

Is the equation below true? How do you know?

$${\mathrm{log}_216={{\mathrm{log}16}\over{\mathrm{log}2}}}$$

Is the equation below true? How do you know?

$${\mathrm{log}_216={{\mathrm{ln}16}\over{\mathrm{ln}2}}}$$

What pattern do you see that you an extrapolate into a general rule?

Guiding Questions

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Target Task


Show that $${\mathrm{log}_{100}x={{\mathrm{log}x}\over{2}}}$$.

Additional Practice


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.

  • Include questions asking students to graph functions like $${y=\mathrm{log}_2x}$$ using the change of base property.
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Lesson 10

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Lesson 12

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Modeling with and Interpreting Exponential Functions

Topic B: Definition and Meaning of Logarithms

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