Using jQuery. Here is jsFiddle I've made http://jsfiddle.net/uQVeN/
HTML:
<base href="www.google.com" />
<div id="valueBefore"></div>
<div id="valueAfter"></div>
JS:
$(document).ready(function(){
$('#valueBefore').text( $('base').attr('href') );
$('base').attr('href','kjhsgdkjahgdjkahgdf');
$('#valueAfter').text( $('base').attr('href') );
});
Will produce:
www.google.com
kjhsgdkjahgdjkahgdf