Never tried this in a webpage, but it work in a browser plugin (where javascripts rights are are not the same for security reasons).
You could definitively go for something like this :
(function(){
var originallog = console.log;
console.log = function(txt) {
// Do really interesting stuff
alert("I'm doing interesting stuff here !");
originallog.apply(console, arguments);
}
})();
The funny thing in javascript is that function are objects too :D
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