Question 1199481
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Let's start with the equation
2*log(x-y) = 4*log(2)+2*log(3)+log(x)+log(y)
and use log rules to say the following shown below.


2*log(x-y) = 4*log(2)+2*log(3)+log(x)+log(y)
log( (x-y)^2 ) = log(2^4)+log(3^2)+log(x)+log(y)
log( (x-y)^2 ) = log(16)+log(9)+log(x)+log(y)
log( (x-y)^2 ) = log(16*9*x*y)
log( (x-y)^2 ) = log(144xy)
(x-y)^2 = 144xy


Then expand out the left side and do a bit of moving terms around
(x-y)^2 = 144xy
x^2-2xy+y^2 = 144xy
x^2+y^2 = 144xy+2xy
x^2+y^2 = 146xy


We started with 
2*log(x-y) = 4*log(2)+2*log(3)+log(x)+log(y)
and ended with 
x^2+y^2 = 146xy


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That process can be done in reverse to go from 
x^2+y^2 = 146xy
to 
2*log(x-y) = 4*log(2)+2*log(3)+log(x)+log(y)


The steps would look like this
x^2+y^2 = 146xy
x^2+y^2 = 144xy+2xy
x^2-2xy+y^2 = 144xy
(x-y)^2 = 144xy
log( (x-y)^2 ) = log(144xy)
log( (x-y)^2 ) = log(16*9*x*y)
log( (x-y)^2 ) = log(16)+log(9)+log(x)+log(y)
log( (x-y)^2 ) = log(2^4)+log(3^2)+log(x)+log(y)
2*log(x-y) = 4*log(2)+2*log(3)+log(x)+log(y)
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