How to describe $x \log (\log x)$? From what I understand, $x \log x$ is usually referred to as 'quasilinear' because it grows increasingly linear as $x$ increases. I was wondering then, if $x \log \log x$ could also be described as 'quasilinear', as it also grows increasingly linear as $x$ increases, and how to describe the difference between $x \log x$ and $x \log \log x$, seeing as both look somewhat similar when graphed (initial 'exponential'looking curve which grows straighter & straighter)

From Wikipedia I see that the definition of quasi-linear is generally functions in $O(n \log(n))$, or in $O(n (\log)^k)$. Since we have that $\log n $ is in $O(n)$, we also get that $n 
\log(\log(n))$ is in $O(n \log n)$. So technically "quasi-linear" would be fine to characterize it using this definition. Big $O$ notation is somewhat off a rough measure since it is only an upper bound though, so if you have a particular application or problem in mind you could look at the complexity a big more closely. 
