<form class="form login" id="log_user">

    <input id="login__username" type="text" name="username" class="form__input" placeholder="Username" required>

    <input id="login__password" type="password" name="password" class="form__input" placeholder="Password" required>

    <input type="submit" value="Log In">

</form>

$(document).ready(function(){
$("#log_user").submit(function(){
    $.ajax({
        type:"POST",
        data:{
            username : $("#login__username").val(),
            password : $("#login__password").val()
            },
        url:"log_user.php",
        success: function(data){
            if(data == 'Success'){
                alert('Login Passw correct');
                }
            else{
                alert(data);
                }
        },
         error: function(){
                alert('something went wrong');
        }
    });
    return false;
});});

<?php

foreach(file('passwd.txt') as $line) {

    if(empty($line)) continue;

    $lineArray = explode(':', $line);
    $username = rtrim($lineArray[0]);
    $password = rtrim($lineArray[1]);

    if( isset($_POST['username']) && isset($_POST['password']) ){

        if($_POST['username'] == $username && $_POST['password'] == $password){
            session_start();
            $_SESSION['user'] = $username;
            echo "Success";
        }
        else{
            echo "Failed";
        }
    }
}

?>

myname:mypassw
myname2:mypassw2