Let $(u_n)_{n\in\mathbb N}$ be the sequence of $3$-smooth numbers (that is whole number that can be written as $2^a3^b$ with $a,b\in\mathbb N$) sorted by increasing order. I am looking for the principal term of the asymptotic of $\log(u_n)$ as well as the error term, for $n\to+\infty$. Any idea to achieve that?

Thanks in advance.