Lets say you are given this limit

$$\lim\_{n\to\infty} ( \log(n + n^n + n^{1/n} )$$

That expression is equal to 
$$\log( \lim\_{n\to\infty}[ n + n^n + n^{1/n}] )
$$
isn't it?

My question is if I could descompose the limit like this without changing the limit like this

$$\log( \lim\_{n\to\infty} n + \lim\_{n\to\infty} n^n + \lim\_{n\to\infty} n^{1/n})
$$

Could I?