If $(x,y)$ is the solution of the following equations $(2x)^log2= (3y)^log3$ and $3^logx = 2^logy$ then x is equal to?

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Answer 1 · 2018-06-03T07:07:43

$x=1/2,y=1/3$

Taking the logarthm on both sides (the first equation) we get
$log(2)(log(2)+log(x))=log(3)(log(3)+log(y))$

Doing the same with the second equation:

$log(y)=log(x)*log(3)/log(2)$
Substituting

$a=log(x)$

we get

$log(x)(log^2(2)-log^2(3))/log(2)=-(log^2(2)-log^2(3))$

so $a=-log(2)$

$log(x)=log(2^(-1))$

$x=1/2$

In the first equation we get

$1=3y$

$y=1/3$

If(x,y) (x,y) is the solution of the following equations (2x)^log2= (3y)^log3(2x)^log2= (3y)^log3 and 3^logx = 2^logy3^logx = 2^logy then x is equal to?