Show $\frac{\ln{(1+nx^2)}}{2n}$ is not uniform convergent on $[0,\infty)$

Question

I've shown that it is pointwise convergent to 0, but I need to show that it is not uniform convergent.

I haven't been able to think of any pair of $x$ values that converge to the same value but $f(x_1)$ and $f(x_2)$ converge to different values because the denominator make it always go to zero.

Is there a way to pick a function of x to compare this to so I can find $\sup{|f_n(x)|}$?

Answer 1

HINT $$f_n(e^n) > 1 {}{}{}{}{}$$