College Algebra
Chapter 5 REVIEW
Evaluate the following:
1
1.
_______________________
log 3
81
Name ______________________________
2.
log 8 64
_________________________
4.
log 121
_________________________
__________________________
3.
3log3 27
5.
log14 22 _________________________
6.
log 8 10
7.
ln e3
8.
log 3 (.333) __________________________
________________________
_________________________
Simplify the following:
9.
a b ( 4a
11.
(3a) −3
a −1b
13.
2 3
 8 
 
 64 
)
2 0
6b 2 a 2
10.
2a −1 8ab 2
12.
−
2
3
14.
3
81a 4
(3b 4 a 3 ) −2
2a −1 8ab −5
Graph the following exponential and Logarithmic equations. State the domain and range. State the y-intercept.
Draw and state the asymptote. (hint: draw parent function before the transformation)
15.
y=
1
x −1
( 4)
2
x
y
Domain: _________________________
Range: ___________________________
Asymptote:
y = _______ (draw it!)
x
16.
1
y = 2⋅  + 2
3
x
y
Domain: _________________________
Range: ___________________________
Asymptote:
17.
y = ________ (draw it!)
y = 4 • 2 x +1 − 3
x
y
Domain: _________________________
Range: ___________________________
Asymptote:
y = ________ (draw it!)
18.
f ( x) = log 3 ( x + 4)
x
y
Domain: _________________________
Range: ___________________________
x-intercept: _______________________
asymptote x = _____________(draw it!!)
19.
f ( x) = log1/2 ( x − 1)
x
y
Domain: _________________________
Range: ___________________________
x-intercept: _______________________
asymptote x = _____________(draw it!!)
20.
f ( x) = log 2 x + 5
x
y
Domain: _________________________
Range: ___________________________
x-intercept: _______________________
asymptote x = _____________(draw it!!)
Expand using the properties of logarithms:
21.
log 3 4x 2 y 5
22.
log6 5x−3 y 4
23.
log
x
2 y3
24.
log
x2
6y
Condense to a single logarithm:
25.
log 2 6 − log 2 3 + log 2 2
26.
log 2 + log x + 3 log 5
27.
5 log x + log y − log15
28.
1
ln 2 + ln(3 − a 2 ) − 2 ln a
6
Solve the following equations: (Round to 2 decimal places if necessary!)
29.
10 2 x+1 = 15
30.
5( x −3) = 5(3 x −5)
31.
e(5 x−6) = 2
31.
log x − log 5 = log 2 x − log( x + 3)
Exponential Growth or Decay Models:
y = a (1 + r )
t
y = a (1 − r )
t
Compound Interest:
A = Pe
rt
 r
A = P 1 + 
 n
nt
32.
While saving up for your first set of wheels, you deposit $4250 into a savings account that pays 3.2%
interest compounded monthly. Will you have enough money in 5 years to buy a car predicted to cost
$5000?
33.
The number of people using MP3 players has drastically reduced since iPods became so popular. In
2007, stores sold an average of 450 MP3 players every month. Sales have declined at a rate of 20% per
month. How many MP3 players will be sold per month in 6 years?
34.
When you were just a wee babe, your parents opened an account for you at a local bank.
The initial deposit was $3000. If the account pays 2.3% annual interest, compounded
continuously, what will the balance in the account be in 18 years, when you graduate
from high school?