Warm-Up: January 31, 2012

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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.

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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 form Logarithmic 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

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
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
Example 11
• Simplify
You-Try #11
• Simplify
Assignment
• Page 377 #1-37 odd, 61-79 odd, 83