Exponential and Logarithmic functions, algebra homework help

Please complete the following questions. It is important that you show all work you did to solve the problems when you submit your work. This includes any calculations, diagrams, or graphs that helped you solve it.

0O
2 x 10″
4 x 10″
6 X 10″
8 x 10″
1 X 102
9-2
Logarithms and
Logarithmic Functions
GET READY for the Lesson
Main Ideas
• Evaluate logarithmic
expressions.
• Solve logarithmic
equations and
inequalities.
Many scientific measurements have such an enormous range of
possible values that it makes sense to write them as powers of 10 and
simply keep track of their exponents. For example, the loudness of
sound is measured in units called decibels. The graph shows the
relative intensities and decibel measures of common sounds.
Sound
New Vocabulary
logarithm
logarithmic function
logarithmic equation
logarithmic inequality
u
Relative
Intensity
100
102
109
10
10
1010
1012
Decibels
40
80
120
0
pin
drop
20
whisper
(4 feet)
60
normal
conversation
100
noisy
kitchen
jet engine
The decibel measure of the loudness of a sound is the exponent or
logarithm of its relative intensity multiplied by 10.
Review
Vocabulary
Logarithmic Functions and Expressions to better understand what is
meant by a logarithm, consider the graph of y = 2* and its inverse. Since
exponential functions are one-to-one, the inverse of y = 2* exists and is
also a function. Recall that you can graph the inverse of a function by
interchanging the x- and y-values in the ordered pairs of the function.
Consider the exponential function y = 2*.
Inverse Relation
when one relation contains
the element (a,
other relation contains the
element (b, a) (Lesson 7-6)
Inverse Function
The inverse function of f(x)
is f-‘(x). (Lesson 7-6)
y
y= 2*
X= 2y
y = 2
х
y
X
у
-3
1
8
-3
(2.4)
y = X
-2
1-2
-1
-1
(0, 11
(4,2)
= 2
0
1
1
0
lo
(1,0)
1
2
2
1
.
Concepts
in Motion
Animation
algebra2.com
As the value of y
decreases, the value
of x approaches 0.
2
4
4
2
3
8
8
3
The inverse of y = 2* can be defined as x = 24. Notice that the graphs of
these two functions are reflections of each other over the line y = x.