Name
LESSON
7-3
Date
Class
Reteach
Logarithmic Functions
A logarithm is another way to work with exponents in equations.
x
If b ⫽ a, then log b a ⫽ x.
If b to the x power equals a,
then x is the logarithm of a in base b.
Use the definition of the logarithm to write exponential equations in logarithmic form and to
write logarithmic equations in exponential form.
Exponential Form
3 4 ⫽ 81
Logarithmic Form
log 3 81 ⫽ 4
base, b ⫽ 3
exponent, x ⫽ 4
value, a ⫽ 81
Logarithmic Form
Exponential Form
base, b ⫽ 5
exponent, x ⫽ 3
value, a ⫽ 125
log 5 125 ⫽ 3
5 3 ⫽ 125
If no base is written for a logarithm, the base is assumed to be 10.
log 100 ⫽ 2 because 10 2 ⫽ 100.
Example:
Assume the base is 10.
Write each exponential equation in logarithmic form.
1. 7 2 ⫽ 49
2. 6 ⫽ 216
3. 2 ⫽ 32
3
b ⫽ 7, x ⫽ 2, a ⫽ 49
log 7 49 ⫽ 2
b⫽
5
6 , x ⫽ 3 , a ⫽ 216
log 6 216 ⫽ 3
b ⫽ 2, x ⫽ 5, a ⫽ 32
log 2 32 ⫽ 5
Write each logarithmic equation in exponential form.
4. log 9 729 ⫽ 3
5. log 2 64 ⫽ 6
b ⫽ 9, x ⫽ 3, a ⫽ 729
9 3 ⫽ 729
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c07-3_rt.indd 22
b ⫽ 2 , x ⫽ 6 , a ⫽ 64
2 6 ⫽ 64
22
6. log 1000 ⫽ 3
b ⫽ 10, x ⫽ 3,
a ⫽ 1000
10 3 ⫽ 1000
Holt Algebra 2
1/4/06 3:38:34 PM
Process Black
Name
Date
Class
Reteach
LESSON
7-3
Logarithmic Functions (continued)
The logarithmic function is the inverse of the exponential function. Use this
fact to graph the logarithmic function.
Graph a function and its inverse.
x
Graph f x ⫽ 0.5 using a table of values.
⫺2
4
x
f x
⫺1
2
0
1
Y
1
0.5
2
0.25
X
Write the inverse function.
⫺1
f x ⫽ log 0.5 x
x and f x switch
places in the function
and its inverse.
The base is 0.5.
F X X
x
⫺1
f
4
⫺2
x 2
⫺1
1
0
0.5
1
Y
YX
0.25
2
Remember, the graph of the inverse
is the reflection of the original function
across the line y ⫽ x.
X
F X LOGX
Complete the tables. Graph the functions.
x
7. f x ⫽ 4
f
x
⫺2
⫺1
0
1
2
f x 1
___
1
__
16
4
1
4
16
⫺1
f
⫺1
x YX
1
___
1
__
16
4
1
⫺2
⫺1
0
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
a207c07-3_rt.indd 23
x ⫽ log 4 x
x
Y
4
16
1
2
23
X
Holt Algebra 2
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