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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 $" "x=3y^2$