How do you prove that $\displaystyle \lim_{x \to +\infty}ln(x) = +\infty$? Starting from the fact that $\displaystyle ln(x)=\int_1^x \frac{dt}{t}$, so without using anything related to $\displaystyle e^x$.

And also that $\displaystyle \lim_{x \to 0}ln(x) = -\infty$.

I just don't understand what my teacher did... Meaningless to me.