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Answer 1 · 2017-06-18T19:13:01

#x=3y^2#

Add #2ln(y)# to both sides of the equation

#ln(x)=ln(3)+2ln(y)#

Exponentiate both sides of the equation

#e^(ln(x))=e^(ln(3)+2ln(y))#

#x=e^(ln(3))e^(2ln(y))#

#x=3e^(ln(y^2))#

#x=3y^2#

Answer 2 · 2017-06-18T20:38:56

A different approach.

#x=3y^2#

Note that #2ln(y)# is the same as #ln(y^2)# so we may write the given equation in the form of:

#ln(x)-ln(y^2)=ln(3)#

Subtraction of logs is the result taking logs of a division of the source values. So we may write this as:

#ln(x/y^2)=ln(3)#

Given that this is true then it is also true that:

#x/y^2=3#

Thus #" "x=3y^2#