Very based question regarding expression transformation.
$$\log p_i \leq \log i + 2 \log\log i $$ $$ p_i \leq i(\log i)^2$$
I am not getting this transformation. So from what I try:
$$\log p_i \leq \log (2i \log\log i) $$ $$ p_i \leq 2i \log\log i$$ $$ p_i \leq 2i \log^2 i$$ $$ p_i \leq \log^2 i^{2i}$$
And I am stuck...