We set the two equations equal to each other and solve for $x$:
\[x^2 \ln x = 4 \ln x\]
This simplifies to $x^2 = 4$, which gives us $x = 2$ and $x = -2$. However, since the domain of the logarithm function is $x > 0$, we discard $x = -2$. So, the intersection
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