Updated Answer
You can do this now using Web Socketing. Here is a guide and hello-wrold example of a php websocket server:
http://socketo.me/docs/hello-world
And to see how to implement client side javascript of websocket, you can see the bottom of the link put above, which shows you this snippet:
var conn = new WebSocket('ws://localhost:8080');
conn.onopen = function(e) {
console.log("Connection established!");
};
conn.onmessage = function(e) {
console.log(e.data);
};
Old
PHP does not support live connections generally in the way you expect, you have to simulate it via repeated AJAX request. How? For instance on each second, or each two seconds.
You first have to write an ajax in your HTML with jQuery library:
Sending a request each second:
var url = "url_to_you_file";
var textarea_id = "#textarea";
setInterval(function(){
$.ajax({
url : "site.com/get-file-logs.php",
type : "POST",
success : function(data){
$(".textarea").html(data);
}
});
}, 1000);
Then in PHP file you would write this:
$file_path = "path_to_your_file";
$file_content = file_get_contents($file_path);
echo $file_content;
The above example gets the file content and sends it back to your browser. You may want to process it in a certain way; that then changes your approach a little bit. Because you must always stick to JSON format when you try to get data back from server to be manipulated by Javascript.