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Math Problems
Algebra 2
Product property of logarithms
(
1
−
a
)
+
3
(
1
−
a
)
2
=
0
\left(1 - a\right)+3\left(1 - a\right)^{2} = 0
(
1
−
a
)
+
3
(
1
−
a
)
2
=
0
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rac{
12
12
12
}{
5
5
5
} imes
6859
6859
6859
-
9687
9687
9687
( ext{sin}
8
8
8
)
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Use the properties of logarithms to expand the following expression.
\newline
log
(
4
(
x
+
6
)
5
x
3
)
\log \left(\frac{4(x+6)^{5}}{\sqrt{x^{3}}}\right)
lo
g
(
x
3
4
(
x
+
6
)
5
)
\newline
Your answer should not have radicals or exponents.
\newline
You may assume that all variables are positive.
\newline
log
(
4
(
x
+
6
)
5
x
3
)
=
\log \left(\frac{4(x+6)^{5}}{\sqrt{x^{3}}}\right)=
lo
g
(
x
3
4
(
x
+
6
)
5
)
=
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14
14
14
. Даны координаты вершин треугольника
A
B
C
:
A
(
1
;
3
)
A B C: A(1 ; 3)
A
BC
:
A
(
1
;
3
)
; *
B
(
2
;
1
)
;
C
(
9
;
3
)
B(2 ; 1) ; C(9 ; 3)
B
(
2
;
1
)
;
C
(
9
;
3
)
. Найдите
\newline
ctg
∠
A
C
B
\operatorname{ctg} \angle A C B
ctg
∠
A
CB
\newline
1
1
1
,
3
3
3
\newline
3
3
3
,
5
5
5
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Simplify each logarithm
\newline
log
3
7
+
log
3
8
\log_{3}7+\log_{3}8
lo
g
3
7
+
lo
g
3
8
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x
→
−
1
lim
x
2
+
2
x
+
1
x
+
1
x \rightarrow -1 \lim \frac{x^2+2x+1}{x+1}
x
→
−
1
lim
x
+
1
x
2
+
2
x
+
1
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The number
y
y
y
is irrational. Which statement about
7
⋅
y
\sqrt{7} \cdot y
7
⋅
y
is true?
\newline
7
⋅
y
\sqrt{7} \cdot y
7
⋅
y
is rational.
\newline
7
⋅
y
\sqrt{7} \cdot y
7
⋅
y
is irrational.
\newline
7
⋅
y
\sqrt{7} \cdot y
7
⋅
y
can be rational or irrational, depending on the value of
y
y
y
.
\newline
Submit
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5
5
5
. If
log
5
a
⋅
log
a
x
=
2
\log _{5} a \cdot \log _{a} x=2
lo
g
5
a
⋅
lo
g
a
x
=
2
, then
x
x
x
is equal to
\newline
(a)
125
125
125
\newline
(d)
25
25
25
\newline
(b)
a
2
a^{2}
a
2
\newline
(d) None of these
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For
y
−
log
1
x
y-\log _{1} x
y
−
lo
g
1
x
to be defined '
a
a
a
' must be
\newline
(a) Any positive real number
\newline
(b) Any number
\newline
(c)
c
c
c
\newline
(d) Any positive real number
1
\quad 1
1
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pgcps.instructure.com/courses/
748004
748004
748004
/assignments/
11147917
11147917
11147917
?module_item_id=
31456298
31456298
31456298
\newline
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\newline
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/
2024
+
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2023 / 2024+Y
2023/2024
+
Y
\newline
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\newline
S
3
3
3
edpuzzle
\newline
Announcements
\newline
Modules
\newline
Grades
\newline
MULTIPLE CHOICE QUESTION
\newline
Which of the following is equivalent to
log
b
8
\log _{b} 8
lo
g
b
8
?
\newline
PGCPS Library
\newline
Resources
\newline
Clever
\newline
Lingco
\newline
Discovery Education
\newline
log
b
(
x
y
)
=
log
b
x
+
log
b
y
\log _{b}(x y)=\log _{b} x+\log _{b} y
lo
g
b
(
x
y
)
=
lo
g
b
x
+
lo
g
b
y
\newline
(
log
b
4
)
(
log
b
2
)
\left(\log _{b} 4\right)\left(\log _{b} 2\right)
(
lo
g
b
4
)
(
lo
g
b
2
)
\newline
log
b
4
+
log
b
2
\log _{b} 4+\log _{b} 2
lo
g
b
4
+
lo
g
b
2
\newline
log
b
4
+
log
b
4
\log _{b} 4+\log _{b} 4
lo
g
b
4
+
lo
g
b
4
\newline
- Previous
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Simplify the expression:
8
+
(
5
3
)
+
x
+
3
=
□
8+(\frac{5}{3})+x+3 = \square
8
+
(
3
5
)
+
x
+
3
=
□
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Make the equation true.
\newline
□
×
□
+
(
□
÷
2
)
=
15
\square \times \square +( \square \div 2)=15
□
×
□
+
(
□
÷
2
)
=
15
\newline
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Which two expressions are equivalent to each other?
\newline
Multi-select Choices:
\newline
(A)
7
6
×
7
2
7^6 \times 7^2
7
6
×
7
2
\newline
(B)
1
7
8
\frac{1}{7^8}
7
8
1
\newline
(C)
7
11
7^{11}
7
11
\newline
(D)
7
12
7
\frac{7^{12}}{7}
7
7
12
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Select all the expressions that are equivalent to
6
2
2
2
\frac{6^2}{2^2}
2
2
6
2
.
\newline
Multi-select Choices:
\newline
(A)
3
0
3^0
3
0
\newline
(B)
1
3
−
2
\frac{1}{3^{-2}}
3
−
2
1
\newline
(C)
3
2
3^2
3
2
\newline
(D)
1
3
2
\frac{1}{3^2}
3
2
1
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Find the volume of the composite solid. *
\newline
13650
13650
13650
cubic inches
\newline
5487
5487
5487
cubic inches
\newline
6825
6825
6825
cubic inches
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If
log
10
y
=
2
3
log
10
x
−
2
\log _{10} y=\frac{2}{3} \log _{10} x-2
lo
g
10
y
=
3
2
lo
g
10
x
−
2
, express
y
y
y
in terms of
x
x
x
with no logarithmic expression.
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17
⋅
x
2
+
5
=
9
2
x
17 \cdot x^{2}+5=\frac{9}{2} x
17
⋅
x
2
+
5
=
2
9
x
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5
5
5
. Select ALL of the correct answers. *
\newline
2
sin
4
θ
+
2
sin
2
θ
⋅
cos
2
θ
=
1
2 \sin ^{4} \theta+2 \sin ^{2} \theta \cdot \cos ^{2} \theta=1
2
sin
4
θ
+
2
sin
2
θ
⋅
cos
2
θ
=
1
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Use logarithms to solve.
\newline
e
2
x
−
e
x
−
56
=
0
e^{2 x}-e^{x}-56=0
e
2
x
−
e
x
−
56
=
0
\newline
Enter the exact answer (i.e. keep your answer in exponential or logarithmic form, you do not need to calculate its numeric value). Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example,
c
∗
ln
(
h
)
c^{*} \ln (h)
c
∗
ln
(
h
)
.
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2
2
2
. Jika x merupakan penyelesaian dari
\newline
Jika
x
x
x
merupakan penyelesaian dari
\newline
3
log
[
3
log
(
x
2
+
3
4
)
]
=
0
{ }^{3} \log \left[{ }^{3} \log \left(\frac{x^{2}+3}{4}\right)\right]=0
3
lo
g
[
3
lo
g
(
4
x
2
+
3
)
]
=
0
\newline
Manakah hubungan yang BENAR antara kuantitas
P
\mathrm{P}
P
dan
Q
\mathrm{Q}
Q
berdasarkan informasi yang diberikan?
\newline
\begin{tabular}{|c|c|}
\newline
\hline
P
\mathbf{P}
P
&
Q
\mathbf{Q}
Q
\\
\newline
\hline
x
\mathrm{x}
x
&
3
3
3
\\
\newline
\hline
\newline
\end{tabular}
\newline
A.
P
>
Q
P>Q
P
>
Q
\newline
B.
Q
>
P
Q>P
Q
>
P
\newline
C.
P
=
Q
P=Q
P
=
Q
\newline
D.
P
=
2
Q
P=2 Q
P
=
2
Q
\newline
E. Informasi yang diberikan tidak cukup untuk memutuskan salah satu dari pilihan di atas
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3
3
3
. Solve and express your answer in both scientific and standard notation. (
4
4
4
pts)
\newline
0.000856
+
(
1.3
×
1
0
−
6
)
0.000856+\left(1.3 \times 10^{-6}\right)
0.000856
+
(
1.3
×
1
0
−
6
)
\newline
Scientific
\qquad
\newline
Standard
\qquad
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Evaluate
2
3
÷
4
×
2
+
3
(
5
−
2
)
2
−
3
×
2
2^{3} \div 4 \times 2+3(5-2)^{2}-3 \times 2
2
3
÷
4
×
2
+
3
(
5
−
2
)
2
−
3
×
2
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3
log
12
+
3
log
24
−
3
log
1
27
3\log{12} + 3\log{24} - 3\log{\frac{1}{27}}
3
lo
g
12
+
3
lo
g
24
−
3
lo
g
27
1
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Evaluate the expression
5
⋅
x
3
x
2
\frac{5 \cdot x^{3}}{x^{2}}
x
2
5
⋅
x
3
for
x
=
2
x=2
x
=
2
\newline
□
\square
□
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sederhanakan fungsi boolean
F
=
w
x
+
x
y
+
y
z
+
z
w
+
w
′
x
′
y
z
′
+
w
′
x
′
y
′
z
F = wx + xy + yz + zw + w'x'yz' + w'x'y'z
F
=
w
x
+
x
y
+
yz
+
z
w
+
w
′
x
′
y
z
′
+
w
′
x
′
y
′
z
dengan melengkapi setiap variabel menggunakan sop lalu menggunakan peta karnaugh
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Simplify to a single trig function with no denominator.
\newline
csc
2
θ
⋅
cos
2
θ
\csc ^{2} \theta \cdot \cos ^{2} \theta
csc
2
θ
⋅
cos
2
θ
\newline
Answer:
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Condense the logarithm
\newline
x
log
b
+
7
log
k
x \log b+7 \log k
x
lo
g
b
+
7
lo
g
k
\newline
Answer:
log
(
□
)
\log (\square)
lo
g
(
□
)
Get tutor help
Evaluate. Write your answer as a whole number or as a simplified fraction.
\newline
3
2
⋅
3
2
=
3^{2} \cdot 3^{2}=
3
2
⋅
3
2
=
\newline
Submit
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log
(
5
x
−
5
)
5
+
log
(
x
−
1
)
2
125
>
2
\log _{(5 x-5)} 5+\log _{(x-1)}{ }^{2} 125>2
lo
g
(
5
x
−
5
)
5
+
lo
g
(
x
−
1
)
2
125
>
2
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Simplify
3
y
4
⋅
2
y
⋅
y
4
3 y^{4} \cdot 2 y \cdot y^{4}
3
y
4
⋅
2
y
⋅
y
4
=
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Problem
\newline
What is the product of all solutions to the equation
\newline
log
7
x
2023
⋅
log
289
x
2023
=
log
2023
x
2023
\log _{7 x} 2023 \cdot \log _{289 x} 2023=\log _{2023 x} 2023
lo
g
7
x
2023
⋅
lo
g
289
x
2023
=
lo
g
2023
x
2023
\newline
(A)
(
log
2023
7
⋅
log
2023
289
)
2
\left(\log _{2023} 7 \cdot \log _{2023} 289\right)^{2}
(
lo
g
2023
7
⋅
lo
g
2023
289
)
2
\newline
(B)
log
2023
7
⋅
log
2023
289
\log _{2023} 7 \cdot \log _{2023} 289
lo
g
2023
7
⋅
lo
g
2023
289
\newline
(C)
1
1
1
\newline
(D)
log
7
2023
⋅
log
289
2023
\log _{7} 2023 \cdot \log _{289} 2023
lo
g
7
2023
⋅
lo
g
289
2023
\newline
(E)
(
log
7
2023
⋅
log
289
2023
)
2
\left(\log _{7} 2023 \cdot \log _{289} 2023\right)^{2}
(
lo
g
7
2023
⋅
lo
g
289
2023
)
2
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Factorise.
x
2
−
2
x
+
1
=
0
x^2 - 2x + 1 = 0
x
2
−
2
x
+
1
=
0
Get tutor help
Express as a single logarithm.
\newline
3
log
a
3
+
7
log
a
5
3\log_{a}3+7\log_{a}5
3
lo
g
a
3
+
7
lo
g
a
5
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u
+
7
7
+
u
−
7
7
\qquad\dfrac{u+7}{7} + \dfrac{u-7}{7}
7
u
+
7
+
7
u
−
7
Get tutor help
(
log
(
x
−
2
)
3
y
)
−
64
−
x
2
−
y
2
\left(\frac{\log(\sqrt{x}-2)}{3y}\right)-\sqrt{64-x^{2}-y^{2}}
(
3
y
lo
g
(
x
−
2
)
)
−
64
−
x
2
−
y
2
Get tutor help
Express the given expression without logs, in simplest form. Assume all variables represent positive values.
\newline
(
1
1
log
11
(
7
w
)
−
log
11
(
9
y
2
)
)
\left(11^{\log _{11}(7 \sqrt{w})-\log _{11}\left(9 y^{2}\right)}\right)
(
1
1
l
o
g
11
(
7
w
)
−
l
o
g
11
(
9
y
2
)
)
\newline
Answer:
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Find the volume of a sphere with a radius of
4
4
4
feet.
\newline
Leave
π
\pi
π
\newline
(A)
341.33
π
f
t
3
341.33 \pi \mathrm{ft}^{3}
341.33
π
ft
3
\newline
(B)
16
π
f
t
3
16 \pi \mathrm{ft}^{3}
16
π
ft
3
\newline
(C)
21.33
π
f
t
3
21.33 \pi \mathrm{ft}^{3}
21.33
π
ft
3
\newline
(D)
85.33
π
f
t
3
85.33 \pi \mathrm{ft}^{3}
85.33
π
ft
3
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Simplify. Your answer should be in proper scientific notation:
\newline
(
2.5
×
1
0
4
)
(
4
×
1
0
3
)
\left(2.5 \times 10^{4}\right)\left(4 \times 10^{3}\right)
(
2.5
×
1
0
4
)
(
4
×
1
0
3
)
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Click and drag like terms onto each other to simplify fully.
\newline
5
x
+
4
x
2
−
6
+
6
+
2
y
+
x
+
4
5 x+4 x^{2}-6+6+2 y+x+4
5
x
+
4
x
2
−
6
+
6
+
2
y
+
x
+
4
Get tutor help
Click and drag like terms onto each other to simplify fully.
\newline
−
5
y
2
+
1
+
3
y
2
−
5
x
+
3
y
2
−
5
y
3
+
7
y
3
-5 y^{2}+1+3 y^{2}-5 x+3 y^{2}-5 y^{3}+7 y^{3}
−
5
y
2
+
1
+
3
y
2
−
5
x
+
3
y
2
−
5
y
3
+
7
y
3
Get tutor help
Condense each expression to a single logarithm.
\newline
2
log
6
u
−
8
log
6
v
2 \log _{6} u-8 \log _{6} v
2
lo
g
6
u
−
8
lo
g
6
v
Get tutor help
Find all values of
x
x
x
.
\newline
log
2
(
2
x
2
+
2
)
−
log
2
(
3
x
+
1
)
=
0
\log_{2}(2x^{2}+2)-\log_{2}(3x+1)=0
lo
g
2
(
2
x
2
+
2
)
−
lo
g
2
(
3
x
+
1
)
=
0
Get tutor help
Evaluate the expression
\newline
(
5
x
3
)
/
(
x
2
)
(5x^{3})/(x^{2})
(
5
x
3
)
/
(
x
2
)
for
x
=
2
x=2
x
=
2
\newline
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Which of the following functions are continuous at
x
=
2
x=2
x
=
2
?
\newline
f
(
x
)
=
x
−
4
4
h
(
x
)
=
log
(
x
−
4
)
\begin{array}{l} f(x)=\sqrt[4]{x-4} \\ h(x)=\log (x-4) \end{array}
f
(
x
)
=
4
x
−
4
h
(
x
)
=
lo
g
(
x
−
4
)
\newline
Choose
1
1
1
answer:
\newline
(A)
f
f
f
only
\newline
(B)
h
h
h
only
\newline
(C) Both
f
f
f
and
h
h
h
\newline
(D) Neither
f
f
f
nor
h
h
h
Get tutor help
5
⋅
7
2
y
=
175
5 \cdot 7^{2 y}=175
5
⋅
7
2
y
=
175
\newline
Which of the following is the solution of the equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
log
7
(
35
)
y=\log _{7}(35)
y
=
lo
g
7
(
35
)
\newline
(B)
y
=
log
35
(
7
)
2
y=\frac{\log _{35}(7)}{2}
y
=
2
l
o
g
35
(
7
)
\newline
(C)
y
=
log
7
(
35
)
2
y=\frac{\log _{7}(35)}{2}
y
=
2
l
o
g
7
(
35
)
\newline
(D)
y
=
log
35
(
7
)
y=\log _{35}(7)
y
=
lo
g
35
(
7
)
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2
⋅
3
2
x
7
=
30
2 \cdot 3^{\frac{2 x}{7}}=30
2
⋅
3
7
2
x
=
30
\newline
Which of the following is the solution of the equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
x
=
7
2
log
3
(
15
)
x=\frac{7}{2} \log _{3}(15)
x
=
2
7
lo
g
3
(
15
)
\newline
(B)
x
=
7
2
log
15
(
3
)
x=\frac{7}{2} \log _{15}(3)
x
=
2
7
lo
g
15
(
3
)
\newline
C)
x
=
7
2
log
30
(
6
)
x=\frac{7}{2} \log _{30}(6)
x
=
2
7
lo
g
30
(
6
)
\newline
(D)
x
=
7
2
log
6
(
30
)
x=\frac{7}{2} \log _{6}(30)
x
=
2
7
lo
g
6
(
30
)
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Which of the following is equivalent to
1
log
3
(
m
)
\frac{1}{\log _{3}(m)}
l
o
g
3
(
m
)
1
?
\newline
Choose
1
1
1
answer:
\newline
(A)
log
m
(
3
)
\log _{m}(3)
lo
g
m
(
3
)
\newline
(B)
log
3
(
m
)
\log _{3}(m)
lo
g
3
(
m
)
\newline
(C)
−
log
m
(
3
)
-\log _{m}(3)
−
lo
g
m
(
3
)
\newline
(D)
−
log
3
(
m
)
-\log _{3}(m)
−
lo
g
3
(
m
)
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Which of the following is equivalent to
log
5
(
m
)
log
15
(
m
)
\frac{\log _{5}(m)}{\log _{15}(m)}
l
o
g
15
(
m
)
l
o
g
5
(
m
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
3
\frac{1}{3}
3
1
\newline
(B)
3
3
3
\newline
(C)
log
(
3
)
\log (3)
lo
g
(
3
)
\newline
(D)
log
5
(
15
)
\log _{5}(15)
lo
g
5
(
15
)
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Which of the following is equivalent to
log
(
3
)
log
n
(
3
)
\frac{\log (3)}{\log _{n}(3)}
l
o
g
n
(
3
)
l
o
g
(
3
)
?
\newline
Choose
1
1
1
answer:
\newline
(A)
log
(
n
)
\log (n)
lo
g
(
n
)
\newline
(B)
log
3
(
n
)
\log _{3}(n)
lo
g
3
(
n
)
\newline
(C)
1
log
(
n
)
\frac{1}{\log (n)}
l
o
g
(
n
)
1
\newline
(D)
1
log
3
(
n
)
\frac{1}{\log _{3}(n)}
l
o
g
3
(
n
)
1
Get tutor help
Which of the following is equivalent to
1
log
b
(
4
)
\frac{1}{\log _{b}(4)}
l
o
g
b
(
4
)
1
?
\newline
Choose
1
1
1
answer:
\newline
(A)
log
b
(
4
)
\log _{b}(4)
lo
g
b
(
4
)
\newline
(B)
log
4
(
b
)
\log _{4}(b)
lo
g
4
(
b
)
\newline
(C)
−
log
b
(
4
)
-\log _{b}(4)
−
lo
g
b
(
4
)
\newline
(D)
−
log
4
(
b
)
-\log _{4}(b)
−
lo
g
4
(
b
)
Get tutor help
1
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