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Contests
National and Regional Contests
USA Contests
USA - Middle School Tournaments
Math Invitational for Girls
2020 MIG
14
14
Part of
2020 MIG
Problems
(1)
2020 Individual #14
Source:
5/1/2022
Given that
x
x
x
satisfies
2
4
x
⋅
2
4
x
⋅
8
4
x
=
1
6
5
2^{4x} \cdot 2^{4x} \cdot 8^{4x} = 16^5
2
4
x
⋅
2
4
x
⋅
8
4
x
=
1
6
5
, find the value of
x
x
x
.
<
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(
A
)
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1
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>
(
B
)
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2
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=
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x
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>
(
C
)
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4
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a
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=
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x
−
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>
(
D
)
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5
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=
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>
(
E
)
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10
<span class='latex-bold'>(A) </span>1\qquad<span class='latex-bold'>(B) </span>2\qquad<span class='latex-bold'>(C) </span>4\qquad<span class='latex-bold'>(D) </span>5\qquad<span class='latex-bold'>(E) </span>10
<
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an
c
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=
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x
−
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′
>
(
A
)
<
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p
an
>
1
<
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a
ss
=
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a
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x
−
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′
>
(
B
)
<
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>
2
<
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a
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=
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l
a
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x
−
b
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d
′
>
(
C
)
<
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>
4
<
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p
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c
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a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
5
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
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>
10
2020 Individual