Algebra 2
Unit 8 Summary Sheet
Name: _______________________
Block: ______ Date: ____________
Rewrite the equation in logarithmic form.
1. 2
5
2. 3
32
4
4
1
3.
2
1
81
16
Rewrite the equation in exponential form.
4. log 4 64
3
5. log 7 1 0
6. log 1 9
2
3
Expand the following:
7.
log5 3x 2 z 3
8. log
7 x3
y
5x2
9. log
y
Condense into a single logarithm.
10. log 6 2log 2 log 3
11. log3 2
1
log3 y
2
Evaluate without a calculator.
13. log3 9
14. log 4 4 4
Use the change of base formula to evaluate.
15. log6 32
16. log9 54
12.
1
ln 8 2 ln 4
3
Solve for x.
17. 53 x
2
19. 4 x
2
21. 52 x
23.
18. 42 x
125
5
16x
3
1
8
20. 4 x 2
30
22. 2log3 x
log 4 x
1
log 4 x 15
32
2 (check for extraneous solutions)
8
4
24. Use the graph of
to obtain the
graph of
. What is the equation
for the asymptote of
26. Use the graph of
?
. What is the domain
?
27. For the graph of
. What is the domain
?
28. Use transformation to graph
. Start with
to obtain the
graph of
and range of
to obtain the
graph of
and range of
25. Use the graph of
.
, what is the
domain and range?
A
D : ( 1, ), R : ( 1, )
B
D:(
, ), R : ( 1, )
C
D:(
, ), R : (
D
D :[ 1, ), R :[ 1, )
, )
29. Use a table of values to prove that
and
are inverse
functions. Then graph these functions.
f(x)
g(x)
30. At an online auction, the opening bid for a pair
of in-line skates is $50. The price of the skates
increases by 10.5% per bid during the next 6
bids.
a. Write a model giving the price p
(in dollars) of the skates after n bids.
c.
According to the model, what will be
the price after 100 bids? Is this
predicted price reasonable? Explain.
b. What was the price after 5 bids?
31. You deposit $2200 in a bank account Find the balance after 4 years for each of the situations described below.
a. The account pays 3% annual interest compounded quarterly.
b. The account pays 2.25% annual interest compounded monthly.
c. The account pays 2% annual interest compounded daily.
32. You buy a new mountain bike for $200. The value of the
bike decreases by 25% each year.
a. Write a model giving the mountain bike’s
value y (in dollars) after t years.
b. Use the model to estimate the value of the
bike after 3 years.
c. Graph the model
d. Estimate when the value of the bike will be $100.
33. You deposit $800 in an account that pays 2.65% annual interest compounded continuously. What is the
balance after 12.5 years?
Answers in Random Order
$ 2406.98
y 200 0.75
log 7 3log x log y
x
4
$1,084, 420.72
log 1 16
x
4
ln
3
1
8
7
2
x
log3
no solution
,
$ 1114.17
1
3
2
1,
x
17
log 2 32
1
81
5
,
1.93
2
y
t
4
70
1
$ 84.38
1
log 5 2log x log y
2
$ 2479.38
2
9
1
6
P 50 1 0.105
x
n
1.06
,
log8
1
4
$82.37
log5 3 2log5 x 3log5 z
log3 2 y
2.41 years
0,
$ 2383.23
1.82
x
16
0,
43
64