I like the use of the theme, and the graphics look nice.
I was going to say that my main issue is that there doesn't seem to be a downside for missing logs so just waiting until I'm sure two logs match works, but now that I played it again paying more attention to the score it looks like that's not the case (so maybe a better indication, like a sound effect, would be good?). I was going to suggest maybe some sort of time limit, so there's an extra challenge of how many logs you can get in a certain amount of time, and that still could be a good idea…
(I think part of what I was thinking about is that for any game of this type, where you can just keep going forever until you lose, there's a risk that the player just won't lose and will get bored, and the fact that you can't lose from just sitting there doing nothing makes this more of an issue. On the other hand, for this game in particular I did in fact lose normally every time I played so maybe it's not as much of an issue as I'd expect?)