Download 9.6

Chapter 9
Exponential and
Logarithmic
Functions
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-1
1
Chapter Sections
9.1 – Composite and Inverse Functions
9.2 – Exponential Functions
9.3 – Logarithmic Functions
9.4 – Properties of Logarithms
9.5 – Common Logarithms
9.6 – Exponential and Logarithmic Equations
9.7 – Natural Exponential and Natural
Logarithmic Functions
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-2
2
§ 9.6
Exponential and
Logarithmic Equations
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-3
3
Solve Exponential and Logarithmic Equations
Properties for Solving Exponential and Logarithmic
Equations
a) If x = y, then ax = ay.
b) If ax = ay, then x = y.
c) If x = y, then logbx = logby (x > 0, y > 0).
d) If logbx=logby, then x = y (x > 0, y > 0).
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-4
4
Solve Exponential and Logarithmic Equations
1
2
Example Solve the equation 8 x  .
1
8 
2
1
3 x
(2 ) 
2
3x
1
2 2
3 x  1
1
x
3
x
Property 6b
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-5
5
Solve Exponential and Logarithmic Equations
Example Solve log 5 2  log 5 (2 x  5)  log 5 (3x  1)
log 5 2  log 5 (2 x  5)  log 5 (3 x  1)
log 5 [2(2 x  5)]  log 5 (3 x  1)
2(2 x  5)  (3 x  1)
Property 6d
x  10  1
x  11
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-6
6
Solve Applications
Example If there are initially 1000 bacteria in a
culture, and the number of bacteria doubles each
hour, the number of bacteria after t hours can be
found by the formula
N  1000(2)
t
How long will it take for the culture to grow to
30,000 bacteria?
continued
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-7
7
Solve Applications
N  1000(2) t
30,000  1000(2) t
30  (2)
t
We want to find the value for t. To accomplish this
we will use logarithms. Begin by taking the
logarithm of both sides of the equation.
continued
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-8
8
Solve Applications
log 30  log( 2) t
log 30  t log 2
log 30
t
log 2
1.4771
t
0.3010
t  4.91
It will take about 4.91 hours for the culture to grow
30,000 bacteria.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-9
9