3 pulleys - 2 masses on incline plane

[Saints-94]

No, you suggested the log would ascend 2m, which means each x would lose 2m. That would mean you start with L=y+2x, And end with a string length (y+1)+2(x-2)=y+2x-3=L-3. The string has mysteriously shrunk by 3m.
Try another way of changing x when y increases by 1m.

(y+1) + 2 (x-0.5) = y + 2x = L ?

 

[haruspex]

(y+1) + 2 (x-0.5) = y + 2x = L ?

Right. The log moves up half the distance that the weight moves down.
Based on that, if the weight descends at speed v, how fast will the log slide up the slope?

 

[Saints-94]

0.5v?

 

[haruspex]

0.5v?

Ok! Now for the one we've been working towards ... how will the accelerations compare?

 

[Saints-94]

Will the acceleration be twice as much at the block compared to the log?

 

[haruspex]

Will the acceleration be twice as much at the block compared to the log?

Yes.
But now I should confess something. The question posed is whether the log will move. To answer that, you do not need to worry about how fast it will move. You can suppose that it does not move, so there are no accelerations, and see whether the balance of forces is consistent with that.
However, most multiple pulley questions do involve different accelerations, and I felt it was important you found out how to deal with these.