Which function is eventually bigger: the cube root function or the natural logarithm function? Visit https://brilliant.org/blackpenredpen/ to start learning and exploring fun Brilliant courses. That link also gives you a 20% off discount on their premium subscription.

In this video, we will compare radical function and logarithmic function: which one is eventually larger? We can take the limit as x goes to the infinity of their ratio. With L'Hospital's Rule, we can see that the cube root of x should be eventually larger. So can we find the other point of intersection?
Here's a lecture on the Lambert W function:    • Lambert W Function (domain, range, ap...  

0:00 sqrt(x) vs. ln(x)
0:39 cbrt(x) vs. ln(x)
4:27 the most satisfying part
4:48 learn more interesting math on Brillaint!
5:47 solving cbrt(x)=ln(x)
9:45 different branches of W(x)

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