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#