natural log notation $\ln^{10}k$

Question

I have a question about some notation I came across in my math text book. I've never seen this before so I'm not sure what it means.

The problem is to use the divergence test to show that an infinite series diverges or show that the test is inconclusive. So, I just have to take the limit of the function.

The infinite series is: $\sum\limits_{k=2}^{\infty}\dfrac{\sqrt{k}}{\ln^{10}k}$

So to use the divergence test to show that the limit equals either 0 or something else, I have:

$\lim\limits_{k\to\infty}\dfrac{\sqrt{k}}{\ln^{10}k}$

This will be $\infty$ over something but I'm not sure what to do with the $\ln^{10}k$ notation. Does it just mean $(\ln(k))^{10}$ similar to how the notation $\cos^2\theta$ means $(\cos\theta)^2$?

Thanks for any help.

Answer 1

Yes this is the same as cosine.