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If log_{x}a + log_{y}a= 4 log_{xy}a then prove x=y

Source: MTRP 2015 Class 11-Short Answer Type Question: Problem 2 :-

September 22, 2020
logarithmsalgebra

Problem Statement

Let x,yx, y be numbers in the interval (0,1) such that for some a>0,a≠1a>0, a \neq 1 log⁡xa+log⁡ya=4log⁡xya\log _{x} a+\log _{y} a=4 \log _{x y} aProve that x=yx=y
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