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2017 AIME Problems
14
My sound when AIME drowns me: logloglog
My sound when AIME drowns me: logloglog
Source: 2017 AIME I #14
March 8, 2017
2017 AIME I
Problem Statement
Let
a
>
1
a > 1
a
>
1
and
x
>
1
x > 1
x
>
1
satisfy
log
a
(
log
a
(
log
a
2
)
+
log
a
24
−
128
)
=
128
\log_a(\log_a(\log_a 2) + \log_a 24 - 128) = 128
lo
g
a
(
lo
g
a
(
lo
g
a
2
)
+
lo
g
a
24
−
128
)
=
128
and
log
a
(
log
a
x
)
=
256
\log_a(\log_a x) = 256
lo
g
a
(
lo
g
a
x
)
=
256
. Find the remainder when
x
x
x
is divided by
1000
1000
1000
.
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