danik.js, так вас устроит
document.getElementById('but').onclick = function() {
var ajax = new XMLHttpRequest();
var params = 'check=' + +document.getElementById('checkbox_jax').checked;
ajax.open('POST', '/auth.php', true);
ajax.setRequestHeader('Content-Type', 'application/x-www-form-urlencoded');
ajax.onreadystatechange = function() {
if (this.readyState == 4 && this.status == 200) {
document.getElementById('res_log').innerHTML = this.responseText;
}
}
ajax.send(params);
return false;
}