2

Part of 2024 AIME

Problems(2)

EZ logarithm V2

Source: 2024 AIME I Problem 2

x

y

x,y>1

\log_x(y^x)=\log_y(x^{4y})=10.

What is the value of

xy

AMCAIMEAIME Ilogarithms

List of positive integers

Source: AIME II 2024 problem 2

A list of positive integers has the following properties: - The sum of the items in the list is

30

. - The unique mode of the list is

9

. - The median of the list is a positive integer that does not appear in the list itself.
Find the sum of the squares of all the items in the list.