Practice problems for third exam
April 11,2015
For #1—6, are the statements true or false?
1.
2.
axaY
-,
a
ax_Y
3. log(zw)
=
log(z)
4. log(zj
=
log(z)w
+
6.
•Tr1€
log(w)
()
Fd
5. log) 1
(z)log(
=log(
(
w)
-J
ft
(A.
aXY
()
3
JO
cJ&Q
V
(ax)Y
pI
7. Write
59285—9005—26
as a rational number in standard form.
q.ago.-LG
5
8. Write (4) as a rational number in standard form.
3
=
9. Write 1, 000, 000 as a rational number in standard form.
,
(ic
10. Write
()
2/3
2
J
Jo
as a rational number in standard form.
(I)
([)
.
()
Q )
5
I0
(
c)
g 000) as a rational number in standard form.
10
o
1
11. Write (1O,
4
fo (ion)
-j) as a rational number in standard form.
log
(
12. Write 5
J
1
(
ijs
/fljc
.
-
(stJ
(50)?
4
13. What is the greatest integer that is less than log
a
5o
=
AfrTSL&JQr
(fj
/e3
-3
14. Solveforxifex=5
X
Ije D
—3. (Write your answer as a rational number in standard form.)
(x)
4
15. Solve for x if log
3
16. Solve for x if 4e
3
E
8.
a
)=
k’je (::)
Page 2
ztIoje(aJ
17. Solve for x if 1og(x + 2) —7
9
=
9
-d
Y-Q
4
18. Solve forxif eX
Q_•y
1. &
R
e
-I
5;(.f
)
je
, (x
1
19. Solve for x if log
2
+
x)
—
2
—
(
(4)
. (x)
1
log
Lcj
(>). 2
(2__.)
( )
)<4
(
—1
Page 3
3
—3(x
20. Graphp(x)
—
2)(x
—
2
2)(x
+
7)
‘S
o
—
<0
—5
1
r(x
—
—
—4
—3
—2
5
—1
+3)
2
2(x+2)(x
—5(x—2)(x—2)
s.
<0
O.—
3
—5
Lecch’ h2al
2’X
vzjr.een)
-:
22. Graph ex and label its y-intercept.
-
Page 4
2
4
5
-
(
23. Graph 1og(x) and label its x-intercept.
24. Graph
e’
—
1 and label its x- and y-intercepts (if there are any).
(C,
I
25. Graph log.(x
+
2) and label its x- and y-intercepts (if there are any).
105e
Page 5
(i))
26. Graph
f
(—1, 2]
27. Graph g: [—2, 1)
—
—
—2x.
R where f(x)
R where g(x)
=
.
2
—x
-
28. Graph g R
—
R where g(x)
=
—x
ifx e (—oa,O)
2
if x
x
ifx e (0,oo)
=
0
Page 6
ifx
29. Graph g : R
—
]R where g(x)
2
2
30. Solve for x if 14x
—
91
<
—
x
if x
(—co,
E
ifx
0)
[0, 2)
[2,oa)
5
—5< —9
5
/7
cJ
ci
14
I
4
I X
31. Solveforxifl—2x+61 <4
—H
—‘
-
,
x t-1
:: ‘o
—
Page 7
32. Consider the following plot depicting a vertical line (in blue):
ctbr
fL L uk’cct Qe
(a) Does this plot depict the graph of a function?
(b) Does this plot depict the solutions of a linear equation in two variabls?
tk2S
= 3?
33. What is the slope of the line 45x
3
—
1}x
.3D
5
34. What is the slope of the line —18x
+
=
4?
35. Is there a unique solution to the following system?
45x
—18x
=
3
=
4
—
+
6y
Cy
U
Page 8
4
vl
hD
c4-
-
L5Lc
36. Find the solution to [lie system of
has a unique solution.)
two
linear equations in two variables. (Hint: The system
S.
-
5x—3y=4
—20
—7x + y
.—
5—’f
x.=
(_)
±s
tx-4
7(±
C
5
4
-o
.—
37. Consider the following system of linear equations in three variables:
—x+7y—8z10
—
5z
=
+ 3z =
x
—
Note: x
=
(a) Is x
y =
—2, y
=
S
5
—5
—
z
1 is a solution of the above system.
0, z
—1 a solution to the above system?
C—aj
-
—
1’
to
o s(- 5’
.
c-a)
-
)(=
(b) Does the al.re system have a unique solution?
/\J 0
(c) Does the above system have infinitely many solutions?
ti
f
c.
Q
I
:
1
Page 9
/
(2,o,IJ
Cv
/