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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
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 function
Logarithmic Function

  • For x>0, b>0, b≠1

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


Converting forms
Converting Forms

Exponential form Logarithmic form

103 = 10003 = log101000

Exponent

Base


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

  • Write in exponential form


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

  • Write in exponential form


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

  • Write in logarithmic form


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

  • Write in logarithmic form


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

  • Evaluate each logarithm


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

  • Evaluate each logarithm




Inverse properties of logs
Inverse Properties of Logs

  • For b>0 and b≠1


You try 5 simplify
You-Try #5 - Simplify


Graphs of f x log b x

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 log b x1
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
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
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
Properties of Logarithms

  • General Properties

  • Common Logarithms

  • Natural Logarithms


Example 11
Example 11

  • Simplify


You try 11
You-Try #11

  • Simplify


Assignment
Assignment

  • Page 377 #1-37 odd, 61-79 odd, 83


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