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Math Invitational for Girls
2020 MIG
14
2020 Individual #14
2020 Individual #14
Source:
May 1, 2022
2020 Individual
Problem Statement
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
.
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
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′
>
(
A
)
<
/
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a
n
>
1
<
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c
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a
s
s
=
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x
−
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>
(
B
)
<
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>
2
<
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a
s
s
=
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a
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e
x
−
b
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′
>
(
C
)
<
/
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a
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>
4
<
s
p
a
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c
l
a
s
s
=
′
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a
t
e
x
−
b
o
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′
>
(
D
)
<
/
s
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a
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>
5
<
s
p
a
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c
l
a
s
s
=
′
l
a
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e
x
−
b
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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
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
4
<
s
p
an
c
l
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
)
<
/
s
p
an
>
10
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