Chapters 6 & 8
Review for Test 3
Name:
Practice these problems.
Study your quizzes, worksheets, examples done in class, and WileyPlus
homework.
1. State the rules of logarithms and inverse properties for each case:
(a) common logarithm
(b) natural logarithm
(c) logarithm with base
b
Solution:
Done in class.
2. Expand.
(a) ln
2
xy
3
z
4
Solution:
ln(2) + ln(
x
) + ln(
y
)

ln(3)

4 ln(
z
)
(b) log
5(
x
+ 3)
√
x

2
Solution:
log(5) + log(
x
+ 3)

1
2
log(
x

2)
3. Contract and simplify.
(a) log(
x
) + log(
x
2
)

log(
yx
)

6 log(
y
)
Solution:
log
x
2
y
7
(b) ln(
p

1) + ln(
r
) + ln(4
p
)

3 ln
p
r
Solution:
ln
4(
p

1)
r
4
p
2
4. Complete Solving for
x
worksheet.
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Chapters 6 & 8
Review
Page 2
Solution:
Done in class.
5. Sketch the function
y
= ln(
x
+ 2)

3.
Solution:
Done in class.
6. What effect does
p
have on the graph of
f
(
x
) = log(
x
p
)? Be specific.
Solution:
f
(
x
) = log(
x
p
) =
p
log(
x
)
If 0
< p <
1,
p
shrinks this function and if
p >
1,
p
stretches this function.
7. Show graphically that
y
= 10
x
and
y
= log(
x
) are inverse functions.
Solution:
Done in class.
8. Write the general equations for:
(a) compounding annually
Solution:
P
(
t
) =
P
0
(1 +
r
)
t
(b) compounding
n
times
Solution:
P
(
t
) =
P
0
1 +
r
n
nt
(c) compounding continuously
Solution:
P
(
t
) =
P
0
e
rt
9. Identify the annual factor for each part in Question 5.
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 Fall '08
 HITCHCOCK
 Quadratic equation, Natural logarithm

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