Hello, and welcome to my recently updated Jax guide! I deleted the old description because it was outdated, and I'm just gonna make a new one that's short and sweet.
The new Jax is pretty damn powerful. 
Empower + 
Leap Strike hit like a nuke, and he can survive a lot longer, which means dishing out more damage. Here we will be going over the basics of the new Jax.
Let's start with items.
Core Build:
This is all Jax needs to hold his own. Good damage from Guinsoo's Rageblade and Bilgewater Cutlass, and good AP from Guinsoo's Reageblade. Enough AS from Guinsoo's Rageblade and 
Relentless Assault. I used to get 
Frozen Mallet on Jax, but now I prefer Bilgewater Cutlass. I also used to get an early The Bloodthirster but Bilgewater Cutlass also replaces this. Bilgewater Cutlass is a cheaper solution to replace both of these items. It provides the slow Frozen Mallet used to supply, and the damage/lifesteal The Bloodthirster supplied. It doesn't give as much survivability as Frozen Mallet but we solve this by getting survivability items earlier than we used to.
Late Game Items:
In later game, we want to get survivability items. The best part about Jax, however, is that he gains damage from survivability. I usually like getting Banshee's Veil before Atma's Impaler so I have more health to work with Atma's Impaler mpassive. It doesn't matter though. If you feel you could use the damage, or if they have a lot of physical damage, then get Atma's Impaler first. After those two items you want The Bloodthirster because it's the best AD item for him, as it will supply him with the lifesteal he needs to stay around, and he is a hoss at farming, so it's easy to stack.
Tips and Tricks:
-Jax isn't that powerful early game. Pretty much all he can do is Empower + Leap Strike combo. He has slow attack speed, and his attacks don't do much damage.
-Once you hit six, you want to be constantly auto attacking the minions to try and keep the stacks on your Relentless Assault. It will make a huge difference in early battles, even if you do end up pushing your lane.
-You can generally farm really easy once you get Relentless Assault. Just attack the minion taking the most damage and you should kill it on your third attack with the bonus damage. It usually turns out to be timed quite perfectly actually.
FAQ
"Why no 
Phantom Dancer?"
Attack speed is wasted on Jax. Guinsoo's Rageblade and Relentless Assault is easily enough. Crit isn't very necessary on Jax either since we aren't getting an 
Infinity Edge. So do we want to pay all that money just for the dodge and movement speed? We can get better bonuses for cheaper. And 20% dodge is good enough.
Build Guide
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