How to hide apex:inputField and Javascript?

Use of apex:inputField with JavaScript

 provides an attribute onchange it binds a JavaScript code to the field onchange event, in this attribute method you can add your JavaScript logic like:
  function onStipulationReasonChange(el){ if(el.value.length > 0){ $('#savebutton3').show(); }else{ $('#savebutton3').hide(); } } 

You can also add onkeyup if only onchange doesn't work for you.

UPDATE

This works with onkeyup here is the code sample: test.vf

              var item = document.getElementById('toggleIt'); function toggleIt(el){ console.log(el.value.length); item.style.display = ((el.value.length > 0)? 'block': 'none'); }  

Test.apxc

  public class Test { public Contact con{get;set;} public Test(){ con = new Contact(); } public PageReference save(){ insert con; return null; } }