Insira o bloco HTML e o conteúdo dinâmico

document.getElementById("log-menu").innerHTML = `
            <a href="#"> 
               ${data.user.email}
            </a>
            <div class="dropdown-menu p-3 dropdown-menu-right">
                <div class="form-group">
                    <label for="email1">Logged in as:</label>
                    <p>${data.user.email}</p>
                </div>
                <button onClick="getLogout()" ">Sign out</button>
            </div>
    `
Idaho Potato