Answer
See graph and explanations.
Work Step by Step
Step 1. Graph $Y_1=log(x^2)$ as shown in the figure (red)
Step 2. Graph $Y_2=2log(x)$ as shown in the figure (green, shifted down a little so not to cover the red)
Step 3. We can see that they are not equivalent. The difference is the domain. For $Y_1$ it is $(-\infty,0)U(0,\infty)$, while for $Y_2$, it is $(0,\infty)$.
