MathDB
What sound does a drowning mathematician make? logloglog...

Source: AIME I 2018 #5

March 7, 2018
AMCAIMEAIME Ilogloglogloglogloglog

Problem Statement

For each ordered pair of real numbers (x,y)(x,y) satisfying log⁡2(2x+y)=log⁡4(x2+xy+7y2) \log_2(2x+y) = \log_4(x^2+xy+7y^2) there is a real number KK such that log⁡3(3x+y)=log⁡9(3x2+4xy+Ky2). \log_3(3x+y) = \log_9(3x^2+4xy+Ky^2). Find the product of all possible values of KK.
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