Сергей Гладышев

var html = '<div><div class="logo"><p>Content</p><p>Further Elaborated</p></div></div>';

var first = $(html).find(".logo")[0].outerHTML;
var second = $(html).find(".logo").prop('outerHTML');
var third = $('<div>').append($(html).find(".logo")).html();
var fourth = $(html).find(".logo").parent().html();

var correct = '<div class="logo"><p>Content</p><p>Further Elaborated</p></div>';

console.log(first);
console.log(second);
console.log(third);
console.log(fourth);

console.log(first === correct && second === first && third === second && fourth === third);