# Warm-Up: January 31, 2012 - PowerPoint PPT Presentation

1 / 24

Warm-Up: January 31, 2012. Suppose that you have \$500 to invest. Which investment yields the greatest return over 6 years: 3.68% compounded semi-annually (twice a year) or 3.65% compounded continuously?. Homework Questions?. Logarithmic Functions. Section 3.2. Logarithmic Function.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

Warm-Up: January 31, 2012

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

### Warm-Up: January 31, 2012

• Suppose that you have \$500 to invest. Which investment yields the greatest return over 6 years: 3.68% compounded semi-annually (twice a year) or 3.65% compounded continuously?

## Logarithmic Functions

Section 3.2

### Logarithmic Function

• For x>0, b>0, b≠1

• The function is the logarithmic function with base “b”

### Converting Forms

Exponential formLogarithmic form

103 = 10003 = log101000

Exponent

Base

### Example 1 (like HW #1-8)

• Write in exponential form

### You-Try #1 (like HW #1-8)

• Write in exponential form

### Example 2 (like HW #12-20)

• Write in logarithmic form

### You-Try #2 (like HW #12-20)

• Write in logarithmic form

### Evaluating Logarithms

• To evaluate logbx, ask, “b to what power gives x?”

• For log232, “2 to what power gives 32?”

• log232 = 5

### Example 3 (like HW #21-30)

• Evaluate each logarithm

### You-Try #3 (like HW #21-30)

• Evaluate each logarithm

### Inverse Properties of Logs

• For b>0 and b≠1

y = x

f (x) = 2x

6

5

4

3

f (x) = log2x

2

-2

-1

2

3

4

5

6

-1

-2

### Graphs of f(x)=logbx

• The x-intercept is 1

• There is no y-intercept

• The y-axis is a vertical asymptote

• If b>1, then the function is increasing

• If 0<b<1, then the function is decreasing

• The graph is smooth and continuous

### Common Logarithm

• A logarithm with base 10 is called the common logarithm.

• The common logarithm is often written without the base

• Use the [LOG] button on your TI-83

### Natural Logarithm

• A logarithm with base e (the natural base) is called the natural logarithm.

• The natural log is usually written with “ln” instead of “log”

• Use the [LN] button on your TI-83

### Properties of Logarithms

• General Properties

• Common Logarithms

• Natural Logarithms

• Simplify

• Simplify

### Assignment

• Page 377 #1-37 odd, 61-79 odd, 83