show all steps and calculate the ratio x/y if

Question

2log₅(x-3y)=log₅(2x)+log₅(2y)

Answer 1

2log(5)(x-3y)=log(5)(2x)+log(5)(2y)

log(5)(x-3y)²=log(5)(2x2y)

(x-3y)²=(2x2y)

(x-3y)²=4xy

x must be greater than 3y

x^2-6xy+9y^2=4xy

x^2-6xy-4xy+9y^2=0

x^2-10xy+9y^2=0

factor

(x-9y)(x-y)=0

x-y=0

x=y

x/y=1 but x>3y implies x/y>3 so disregard this answer

x-9y=0

x=9y

x/y=9 is the ratio