I think that a couple of cheap wedges that fit in your pocket, and won't ruin a chain if you hit 'em would do the same job much cheaper and easier, with the back-up for if one wanted to pop out.
Then you can use the same wedges for bucking the log.
Wouldn't want to try to fit that hydraulic jack in my pocket.
For that application, I'd just as soon use a 20 ton bottle jack that will also jack up a truck, backed up with wedges of course.
My bottle jack was $30-40. Wedges less than $20.