Lesson Plan #6
Lesson Plan #58
Class: Intuitive Calculus Date: Wednesday February 9th, 2011
Topic: Review of Logarithmic Functions Aim: How do we use logarithmic functions?
Objectives:
1) Students will be able to use logarithmic functions
HW# 58:
1) Use the properties of logs to write [pic]
2) Write the expression [pic]
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]
Sample Test Questions:
1) The range for [pic]is
A) [pic] B) [pic] C) [pic] D) [pic]
E) [pic]
-----------------------
Properties of logs
[pic]
[pic]
[pic]
log
log
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