2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121....
TRANSCRIPT
![Page 1: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/1.jpg)
Math 106: Worksheet 15
Simplify.
1.(a3b4c5)4
(a2b3c4)2
a8b10c12
2. (−2x3)0
1
3. (−2x2y3)4(4xy3)
64x9y15
4. (2x− y)0
1
5. 2 · 50 − 5
−3
6.6x−5
5y−1
6y
5x5
7.
(x−4
9−1
)2
81
x8
8.
(6ab−2
3a2b−4
)3
8b5a3
9.a−2c3
2b−5
b5c3
2a2
10.
(c−4c−2
c−6c8
)−4
c32
1
![Page 2: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/2.jpg)
11. (z − 7)(z + 7)
z2 − 49
12. (a− 4)(a+ 4)
a2 − 16
13. (w + 8)2
w2 + 8w + 64
14. (r + 10)2
r2 + 20r + 100
15. (j − 5)2
j2 − 10j + 25
16. (h− 4)2
h2 − 8h+ 16
17. (2b2 − 1)(2b2 + 1)
4b4 − 1
18. (1− 3c)2
1− 6c+ 9c2
Factor.19. a2 − 4
(a− 2)(a+ 2)
20. b2 − 9
(b− 3)(b+ 3)
21. c2 − 36
(c− 6)(c+ 6)
2
![Page 3: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/3.jpg)
22. 2d3 − 98d
2d(d− 7)(d+ 7)
23. j3 − jk2
j(j − k)(j − k)
24. 32x2y − 2y3
2y(4x− y)(4x+ y)
Solve.
25.z
z − 2− 1
z + 5=
7
z2 + 3z − 10
z = 1
26.3
p− p+ 3
3p=
2p− 1
2p− 5
6
p = 5
27.4
c− 2− 1
2− c=
25
c+ 6
c = 4
28.−3
w + 2=
w
w + 2
w = −3
Simplify.
29.
1
x+ 1+ 1
3
x+ 1+ 3
1
3
30.
1− 3
y + 1
3 +1
y + 1y − 2
3y + 4
31.x− x− 6
x− 1
x− x+ 15
x− 1
3
![Page 4: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/4.jpg)
x2 − 2x+ 6
(x− 5)(x+ 3)
32.
1
z − 3− 4
z3
z − 3+
1
z12− 3z
4z − 3
33.
2
r − 1− 3
r + 14
r + 1+
5
r − 15− r
9r + 1
Find the domain of each expression.
34.√2x− 5
[5
2,∞)
35.√3x+ 12
[−4,∞)
36.√x+ 5
[−5,∞)
37.√x
[0,∞)
Simplify the complex fractions.
38.
3
2m+
4
3m1
4m− 5
9m102
11
39.
1
x+ 1+ 1
3
x+ 1+ 3
1
3
4
![Page 5: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/5.jpg)
40.
1− 3
y + 1
3 +1
y + 1y − 2
3y + 4
50.z − z − 6
z − 1
z − z + 15
z − 1z2 − 2z + 6
(z − 5)(z + 3)
51.
1
q − 3− 4
q3
q − 3+
1
q12− 3q
4q − 3
52.
2
p− 1− 3
p+ 14
p+ 1+
5
p− 15− p
9p+ 1
Solve each equation.
53.14
a2 − 1+
1
a− 1=
3
a+ 1
9
54. b− 3b
2− b=
6
b− 2
−3
55.c
6=
3c
11
0
56.3
p− p+ 3
3p=
2p− 1
2p− 5
6
5
57.h+ 17
h2 − 1− 1
h+ 1=
h− 2
h− 1
5
![Page 6: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/6.jpg)
−4, 5
58.3
k − 2− 5
k + 3=
1
k2 + k − 6
9
59.5
2m+ 6− 1
m+ 1=
1
m+ 3
3
Simplify60.
√8w3y3
2wy√2wy
61. 3√
48x3y8z7
2xy2z2 3√
6y2z
62.3
√−27y36
1000
−3y12
10
63.
√9a2
49b2
3a
7b2
64.
2a12
b13
6
64a3
b2
65. (km12 )3(k3m5)
12
k92m4
66. (m14n
12 )2(m2n3)
12
m32n
52
67.
(a−1m b
−1n
)−mn
6
![Page 7: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/7.jpg)
anbm
68.(a−m2 b
−n3
)−6
a3mb2n
69.
(a−3mb−6n
a9m
)−13
anbm
70.
a−3m b
6n
a−6m b
9n
−13
b1n
a1m
Simplify.
71.√2t5 ·√10t4
2t4√5t
72. (3√2−√3)(2√2 + 3
√3)
3 + 7√6
73. (5√j − 3)2
25j − 30√j + 9
74. 10√m−
√16m
6√m
75. 5√z2x− 7
√z2x+ 6
√z2x
4z√x
Simplify. Rationalize denominators if needed.
76.1 +√2√
3− 1√2 +√3 +√6 + 1√
4
7
![Page 8: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/8.jpg)
77.6
3−√18
−2− 2√2
78.5√
7−√5
5√7 + 5
√5
2
79.
√mn√
m+ 3√n
m√n− 3n
√n
m− 9n
80.√y√y − 3+
x2 + 8x√x− 45
√x
x(x− 9)
Solve the equation for the give variable.
81. 2√q + 4 = 5
q =9
4
82.√4r2 + r − 3 = 2r
r = 3
83. s−12 = 9
s =1
81
84. (t− 3)23 = −4
85. (u+ 2)4 = 32
u = 2 4√2± 2
86.√5r − r2 =
√6
r = 2, 3
87.√q − 3 =
√q + 2− 1
8
![Page 9: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/9.jpg)
q = 7
88. 1 +√y + 7 =
√2y + 7
y = 9
89. 2√p−√p− 3 = 3
p = 4
90.√c−√c− 1 = 1
c = 1
91.√d+ 4− 2
√d− 1 = −1
d = 5
Simplify.
92. (2 + i)(3 + 4i)
2 + 11i
93. i25
i
94.6
7− 2i
42 + 12i
53
95. 2√−20−
√−45
i√5
96.−4 +
√−32
2
−2 + 2i√2
Complete the square.
97. q2 + 2q
9
![Page 10: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/10.jpg)
q2 + 2q + 1
98. r2 + 14
r2 + 14r + 49
99. s2 − 3s
s2 − 3s+9
4
100. t2 − 5t
t2 − 5t+25
4
101. u2 +1
4u
u2 +1
4u+
1
64
102. v2 +3
2v
v2 +3
2v +
9
16
103. w2 +2
3w
w2 +2
3w +
1
9
104. p2 +6
5p
p2 +6
5p+
9
25
Factor each perfect square polynomial.
105. x2 + 8x+ 16
(x+ 4)2
106. x2 − 10x+ 25
(x− 5)2
107. x2 − 5x+25
4(x− 5
2
)2
10
![Page 11: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/11.jpg)
108. x2 + x+1
4(x+
1
2
)2
109. y2 − 4
7y +
4
49(y − 2
7
)2
110. y2 − 6
5y +
9
25(y − 3
5
)2
111. y2 +3
5y +
9
100(y +
3
10
)2
112. y2 +3
2y +
9
16(y +
3
4
)2
Complete the square to solve:
113. q2 + 5q = 14
q = −7, 2
114. w2 − w − 20
w = −4, 5
115. 4x2 − 4x− 1 = 0
x =1±√2
2
116. y2 = −1
2
y = ±i√2
2
117. 5z2 − 4z + 1 = 0
z =2± i
5
11
![Page 12: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/12.jpg)
118. c2 + 4c = 6
c = −2±√10
119. d2 + 6d− 8 = 0
d = −3±√17
120. a2 + 8a− 4 = 0
a = −4±√5
121. b2 + 10b− 3 = 0
b = −2±√10
Use the Quadratic Formula: (Rearrange the equation to use the quadratic formula ifneeded.)
122. −8q2 − 2q + 1 = 0
q = −1
2,1
4
123. −6z2 + 7z + 3 = 0
z = −1
3,3
2
124. 16x2 + 24x+ 9
x = −3
4
125.1
3t2 − t+
1
6= 0
t =3±√7
2
126.9(3x− 5)2
4= 1
x =13
9,17
9
127.1
4y2 + y = 1
y = −2± 2√2
12
![Page 13: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/13.jpg)
128.1
3p2 +
1
2p =
1
3
p = −2, 12
129.25(2r + 1)2
9= 0
r = −1
2
130.m
3m− 4=
2
m+ 4
m = 1± i√7
131. n =7n− 4
12(n− 1)
n =1
4,4
3
Solve the problem that is quadratic in form(Think substitution)
132. (2x− 1)2 − 4(2x− 1) + 2 = 0
x =3±√2
2
133. x4 − 20x2 + 64 = 0
x = ±2,±4
134. x4 − 13x2 + 36 = 0
x = ±2,±3
135. x6 + 7x3 = −8
x = −2, 1
136. x6 − 28x3 + 27 = 0
x = 1, 3
137. x− 3x12 + 2 = 0
x = 1, 4
138. x23 + 4x
13 + 3 = 0
13
![Page 14: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/14.jpg)
x = −27,−1
139. x12 − 5x
14 + 6 = 0
x = 16, 81
140. x−2 + x−1 − 6 = 0
x = −1
3,1
2
141. x−2 − 2x−1 = 8
x = −1
2,1
4
142.
(1
y − 1
)2
+
(1
y − 1
)= 6
y =2
3,3
2
143.
(1
w + 1
)2
− 2
(1
w + 1
)− 24 = 0
y = −5
6,−5
4
144. Which way does the graph open?
y = −3x2 + 4x+ 2
down
145. Which way does the graph open?
y = 2x2 + 4x+ 8
up145. Which way does the graph open?
y = (10− x)2
down146. Which way does the graph open?
y = 5x2 + 13x+ 24
up
14
![Page 15: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/15.jpg)
147. Which way does the graph open?
y = (x+ 6)2
up148. Graph:
y = −2x2 + 5
149. Graph:
y = (x+ 3)2
150. Find the vertex.
y = x2 + 8x− 3
vertex = (−4,−19)
151. Find the vertex.
y = −3x2 + 18x− 7
vertex = (3, 20)
152. Find the vertex.
y = x2 − x+ 1
vertex =
(1
2,3
4
)153. Find the intercepts.
y = 16− x2
x− int = (−4, 0), (4, 0)
y − int = (0, 16)
154. Find the intercepts.
15
![Page 16: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/16.jpg)
y = x2 − x− 6
x− int = (−2, 0), (3, 0)
y − int = (0,−6)
155. Find the intercepts.
y = −4x2 + 12x− 9
x− int = (3
2, 0)
y − int = (0,−9)
156. Determine the domain and the range.
f(x) = x+ 1
Domain: (−∞,∞)
Range: (−∞,∞)
157. Determine the domain and the range.
f(x) = 5− x
Domain: (−∞,∞)
Range: (−∞,∞)
158. Determine the domain and the range.
f(x) =√x− 2
Domain: [2,∞)
Range: [0,∞)
159.Determine the domain and the range.
f(x) =√x+ 4
Domain: [−4,∞)
Range: [0,∞)
16
![Page 17: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/17.jpg)
160. Determine the domain and the range.
f(x) =√2x
Domain: [0,∞)
Range: [0,∞)
161. Determine the domain and the range.
f(x) =√2x− 4
Domain: [2,∞)
Range: [0,∞)
162. Let f(x) = 4x− 3 and g(x) = x2 − 2x .
Find the following.
a. (f + g)(x)b. (f − g)(x)c. (f · g)(x)d. (
f
g)(x)
e. (f + g)(3)f. (f − g)(−3)g. (f · g)(−1)h. (
f
g)(4)
a. x2 + 2x− 3b. −x2 + 6x− 3c. 4x3 − 11x2 + 6x
d.4x− 3
x2 − 2xe. 12f. −30g. −21h.
13
8
163. Let f(x) = 2x− 3 , g(x) = x2 + 3x , h(x) =x+ 3
2a. (fof)(x)
b. (gog)(x)c. (hoh)(x)d. (fog)(−2)
17
![Page 18: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/18.jpg)
e. (gof)(1)f. (foh)(x)g. (hof)(x)h. (fofof)(x)
a. 4x− 9b. x4 + 6x3 + 12x2 + 9x
c.x+ 9
4d. −7e. −2f. xg. xh. 8x− 21
Find the inverse of the indicated function.
164. f(x) = 5x
f−1(x) =x
5
165. j(x) = x+ 7
j−1(x) = x− 7
166. r(x) = 2x− 8
r−1(x) =x+ 8
2
167. m(x) =2
x
m−1(x) =2
x
168. z(x) = 3√x− 4
z−1(x) = x3 + 4
169. n(x) =2
x+ 1
n−1(x) =2
x− 1
170. u(x) = 3√3x+ 7
u−1(x) =x3 − 7
3
18
![Page 19: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/19.jpg)
171. h(x) =1− x
x+ 3
h−1(x) =1− 3x
x+ 1
172. g(x) =x+ 1
x− 2
g−1(x) =2x+ 1
x− 1
173. k(x) = 2 3√x− 1
k−1(x) =
(x+ 1
2
)3
174. If f−1(x) is truly an inverse of f(x) then fof−1(x) =1
x. True or False.
False . If f−1(x) is truly an inverse of f(x) then fof−1(x) = xSolve the equation.
175. 2x = 64
x = 6
176.
(1
3
)x
= 9
x = −2
177. 10x =1
100
x = −2
178. −32−x = −81
x = −2179. 42x−1 = 16
x =3
2
180.
(1
4
)3x
= 16
x = −2
3
Write each exponential equation as a logarithm equation and each logarithm equationas an exponential.
19
![Page 20: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/20.jpg)
181. log2(8) = 3
23 = 8
182. logc(t) = 4
c4 = t
183. logb(N) = m
bm = N
184. log(100) = 2
102 = 100
185. e3 = x
ln(x) = 3
186. m = ex
ln(m) = x
187. 53 = 125
log5(125) = 3
188. log3(x) = 10
310 = x
189. a3 = c
loga(c) = 3
190. 2a = b
log2(b) = a
Simplify (Inverses)
191. log2(210)
10
20
![Page 21: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/21.jpg)
192. ln(e9)
9
193. 5log5(15)
15
194. log(108)
8
195. eln(4)
4
196. 3log3(20)
20Write as as single logarithm and simplify. (Product Rule)
197. log(3) + log(7)
log(21)
198. ln(5) + ln(4)
ln(20)199. log3(
√5) + log3(
√x)
log3(√5x)
200. ln(a3) + ln(a5)
ln(a8)
201. ln(2) + ln(3) + ln(5)
ln(30)
202. log2(x) + log2(y) + log2(z)
log2(xyz)
203. log(x) + log(x+ 3)
21
![Page 22: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/22.jpg)
log(x2 + 3x)
204. ln(x− 1) + ln(x+ 1)
ln(x2 − 1)
205. log3(x− 4) + log3(x− 5)
log3(x2 − 9x+ 20)
Write as as single logarithm and simplify. (Quotient Rule)
206. log(8)− log(2)
log(4)
207.ln(3)− ln(6)
ln
(1
2
)208. log2(x
6)− log2(x2)
log2(x4)
209. log3(x2 − 9)− log3(x− 3)
log3(x+ 3)
210. ln(x2 + x− 6)− ln(x+ 3)
ln(x− 2)
Write each expression in terms of log(3). (Power Rule)
211. log(27)
3log(3)
212. log
(1
9
)−2log(3)
213. log(√3)
22
![Page 23: 2x y 3 (4xy118. c2 +4c = 6 c = 2 p 10 119. d2 +6d 8 = 0 d = 3 p 17 120. a2 +8a 4 = 0 a = 4 p 5 121. b2 +10b 3 = 0 b = 2 p 10 Use the Quadratic Formula: (Rearrange the equation to use](https://reader033.vdocuments.mx/reader033/viewer/2022041702/5e4248d30c58823b7d4ea740/html5/thumbnails/23.jpg)
1
2log(3)
214. log(3x)
xlog(3)
215. log(3100)
100log(3)
Solve the logarithmic equation.
216. log(x− 5) = 2
x = 105
217. log2(x+ 1) = 3
x = 7
218. 4log3(2x)− 1 = 7
x =9
2
219. ln(x) + ln(x+ 5) = ln(x+ 1) + ln(x+ 3)
3
220. log(x) + log(x+ 5) = 2 · log(x+ 2)
4
23