Lesson Plan #6



Lesson Plan #40

Class: PreCalculus Date: Thursday December 5th, 2013

Topic: Review of Logarithmic Functions Aim: How do we use logarithmic functions?

Objectives:

1) Students will be able to use logarithmic functions

HW# 40:

Page 475 #’s 4, 8, 14, 18, 24, 30, 34, 46, 56, 62

Do Now: On your graphing calculator, sketch the graph of [pic]

Sketch the graph of the inverse of [pic]

What is the equation of the inverse of [pic]?

Procedure:

Write the Aim and Do Now

Get students working and take attendance

Give back work

Go over the HW

Collect HW

Go over the Do Now

The inverse of [pic]is [pic].

In [pic], y is the exponent with base [pic]that gives us x. Another word for exponent is a logarithm.

So we can rewrite y = the logarithm with base [pic]that gives us x. We can abbreviate this as

[pic], which equals what we started with [pic]

So [pic]

Or in general, [pic]

Assignment #1:

Write the logarithmic equation in exponential form

A) [pic] B) [pic]

C) [pic]

Assignment #2:

Write the exponential equation in logarithmic form.

A) [pic] B) [pic]

C) [pic]

Assignment #3:

Evaluate

A) [pic] (meaning, 2 raised to what power equals 32?)

B) [pic] C) [pic]

D) [pic]

Assignment #4:

Solve for x

A) [pic] B) [pic]

The logarithmic function with base 10 is called the common log. An example is [pic]. Common logs are usually written without the base. If a log is written without the base, it is a common log which has a base of 10. Common logs can be evaluated with the calculator using the button.

Assignment #5:

Use the calculator to evaluate

A) log 10 B) log 2.5

C) log 145

Another widely used base, aside from 10, is [pic]. For example we could have

[pic]. Find x.

The logarithmic function with base [pic]is called the natural logarithmic function. As such, [pic]is written as [pic].

Assignment #6:

A) Write the logarithmic equation [pic]in exponential form

B) Write the exponential equation [pic] in logarithmic form

C) Evaluate

i) [pic] ii) [pic]

iii) [pic]

D) Use a calculator to evaluate

i) [pic] ii) [pic]

Assignment #7:

A) The population of a town will double in [pic]years. Find [pic]

Assignment #8:

Students in a mathematics class were given an exam and then tested monthly with an equivalent exam. The average score for the class was given by the human memory model [pic], [pic], where [pic]is the time in months.

A) What was the average score of the original exam ([pic])?

B) What was the average score after 4 months?

C) What was the average score after 10 months?

Assignment #9:

Most calculators have only two types of log keys; one for common logs (base 10) and one for natural logs (base [pic]). You may occasionally need to evaluate logs with other bases. To do this, use the change of base formula

[pic]

When using the change of base formula, “commonly”, you change the base to 10 since your calculator has a base 10 log button, namely the button.

Using the change of base formula, evaluate

A) [pic]

B) [pic]

Assignment #10:

Let’s prove a property of logs. Let’s start with [pic]and [pic].

From here we get [pic], which gives us [pic]. Write this in logarithmic form and we get[pic]

Take the original two equations and write them in logarithmic form, namely, [pic]and [pic].

So we now get [pic]

A) Use the properties of logs to write the expression as a sum, difference, and/or constant multiple of logarithms.

[pic]

B) Write the expression as the logarithm of a single quantity

[pic]

Assignment #11:

Solve for x: [pic]

Assignment #12:

Simplify [pic]

Assignment #13:

Solve for x: [pic]

Assignment #14:

Find the domain of the function [pic]

Assignment #15:

Use your graphing calculator to sketch the graph of [pic]

(Note the base)

Assignment #16:

Find the inverse of the function [pic]

Assignment #17: Find the domain and range of each function [pic]

-----------------------

log

log

Properties of logs

[pic]

[pic]

[pic]

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