I'm learning about the analysis of algorithms and I'm encountering some steps in an explanation which I can't quite understand (log is a logarithm with base 2 in this context).

The step from the second to third doesn't quite click, but it goes on:

The above step is a bit hazy too...

Which is a worst-case running time of

Basically I'm lacking insight into alot of the simplifications/reductions/steps taken to come to I would very much appreciate some clarification on steps taken so I can apply this when I need to analyze algorithms myself