7.3 - Logarithmic Functions as Inverses

7.3 - Logarithmic Functions as Inverses

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Objectives

• To write and evaluate logarithmic expressions

• To graph logarithmic functions

What's a "log"?

Let's practice:

Another way to think about it:

The log is the exponent.

The base is the base.

Multiple Choice

Write the equation in exponential form: $$\log_39=2$$

• $$3^9=2$$

• $$2^3=9$$

• $$3^2=9$$

• $$9^2=3$$

Math Response

Write the equation in exponential form: $$\log_71=0$$

Type answer here

Correct Answer: 7^0=1

Deg^°

Rad

Multiple Choice

Write the equation in log form: $$14^2=196$$

• $$\log_{196}14=2$$

• $$\log_214=196$$

• $$\log_{14}2=196$$

• $$\log_{14}196=2$$

Math Response

Write the equation in log form: $$36^{\frac{1}{2}}=6$$

Type answer here

Correct Answer: \log_{36}\left(6\right)=\frac{1}{2}

Deg^°

Rad

If you felt like that last one was kind of challenging

Here's a quick memory device:

Image courtesy the great Amy Gruen's blog "square root of negative one teach math"

Poll

Select the image that most closely represents your feelings about how well you understand how to write and convert log expressions:

Independent Practice

At your table groups begin work on the 7.3 Practice - Logarithmic Functions as Inverses handout. I will be around to peek over shoulders and answer questions.

Multiple Choice

Write the exponential in log form: $$9^2=81$$  

• $$\log_2\ 9=81$$  

• $$\log_9\ 81=2$$  

• $$\log_{81}\ 9=2$$  

• $$\log_9\ 2=81$$  

Multiple Choice

Evaluate the expression: $$\log_5\ 1$$  

• 1

• 5

• 0

• undefined

Multiple Choice

Write the log in exponential form: $$\log_{\frac{1}{2}}8\ =\ -3$$  

• $$\left(\frac{1}{2}\right)^8=-3$$  

• $$8^{\frac{1}{2}}=-3$$  

• $$8^{-3}=\frac{1}{2}$$  

• $$\left(\frac{1}{2}\right)^{-3}=8$$  

Multiple Choice

Write the log as an exponential: $$\log_{12}\ 144=2$$  

• $$\sqrt{144}=12$$  

• $$12^2=144$$  

• $$\frac{144}{12}=2$$  

• $$2^{12}=144$$  

Common log

Open Ended

Rewrite $$\log\ 1000$$  as an exponential.

So it kind of looks like logs and exponentials "undo" each other?

Inverse functions are reflected across the line y = x, which is indicated as the black dotted line on the graph.

After our break we'll get a chance for independent practice.