Master pages are are also webforms, except that it will combine with content pages to form a single page at runtime. You'll need to put any server control inside <form runat="server"></form>
. After you've made this, you don't need to add tags on other pages which is content page of this master page.
As of now, you can solve your problem by adding a
<form runat="server">
<asp:LinkButton ID="LinkButton1" runat="server" onclick="LinkButton1_Click">Logout</asp:LinkButton>
</form>
Put the ContentPlaceholder control inside the form tag
Remove <form>
tag from content page