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2024 AIME
2
EZ logarithm V2
EZ logarithm V2
Source: 2024 AIME I Problem 2
February 2, 2024
AMC
AIME
AIME I
logarithms
Problem Statement
Real numbers
x
x
x
and
y
y
y
with
x
,
y
>
1
x,y>1
x
,
y
>
1
satisfy
log
x
(
y
x
)
=
log
y
(
x
4
y
)
=
10.
\log_x(y^x)=\log_y(x^{4y})=10.
lo
g
x
(
y
x
)
=
lo
g
y
(
x
4
y
)
=
10.
What is the value of
x
y
xy
x
y
?
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