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Warm-Up: January 31, 2012PowerPoint Presentation

Warm-Up: January 31, 2012

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Warm-Up: January 31, 2012

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- 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

- For x>0, b>0, b≠1
- The function is the logarithmic function with base “b”

Exponential formLogarithmic form

103 = 10003 = log101000

Exponent

Base

- Write in exponential form

- Write in exponential form

- Write in logarithmic form

- Write in logarithmic form

- To evaluate logbx, ask, “b to what power gives x?”
- For log232, “2 to what power gives 32?”
- log232 = 5

- Evaluate each logarithm

- Evaluate each logarithm

- 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

- 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

- 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

- 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

- General Properties

- Common Logarithms

- Natural Logarithms

- Simplify

- Simplify

- Page 377 #1-37 odd, 61-79 odd, 83