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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
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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