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

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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• 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 form Logarithmic 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

You-Try #5 - Simplify

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

• 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