[tex]
\lim_{x\to\infty}(x-\ln(x)^2) \\
\lim_{x\to\infty}(x-2\ln(x)) \\
\lim_{x\to\infty}\Big(x\Big(1-\dfrac{2\ln(x)}{x}\Big)\Big) \\
\lim_{x\to\infty}x\cdot\lim_{x\to\infty}\Big(1-\dfrac{2\ln(x)}{x}\Big) \\
\infty\cdot\Big(\lim_{x\to\infty}(1)-\lim_{x\to\infty}\Big(\dfrac{2\ln(x)}{x}\Big)\Big) \\
\infty\cdot(1-2\lim_{x\to\infty}(1/x)) \\
\infty\cdot(1-0) \\
\infty\cdot1=\boxed{\infty}
[/tex]
Hope this helps.
