Refer the below sample code how to generate Log in notepad file. I referred same Question code.

Download Multiple (Bulk) Files from FTP folder in ASP.Net using C# and VB.Net and implemented the Generating Log in notepad file You can refer this both article for your reference to refer how to log the file.

Error logging and Exception handling in ASP.Net using C# and VB.Net

Write to Log File (Text File) using Windows Service in C# and VB.Net

C#

protected void DownloadMultipleFileAsZip(object sender, EventArgs e)
{
    List<Files> fileList = new List<Files>();
    foreach (GridViewRow row in gvFiles.Rows)
    {
        if ((row.FindControl("chkSelect") as CheckBox).Checked)
        {
            string fileName = row.Cells[1].Text.Trim();
            string ftp = "ftp://yourserver.com/";
            string ftpFolder = "Uploads/";
            try
            {
                WebClient request = new WebClient();
                string url = ftp + ftpFolder + fileName;
                request.Credentials = new NetworkCredential("Username", "Password");
                byte[] bytes = request.DownloadData(url);
                fileList.Add(new Files() { FileName = fileName, Bytes = bytes });
            }
            catch (WebException ex)
            {
                throw new Exception((ex.Response as FtpWebResponse).StatusDescription);
            }
        }
    }

    using (ZipFile zip = new ZipFile())
    {
        zip.AlternateEncodingUsage = ZipOption.AsNecessary;
        zip.AddDirectoryByName("Files");
        foreach (Files file in fileList)
        {
            zip.AddEntry(file.FileName, file.Bytes);
        }

        LogFile(string.Format("Total files {0} and downloaded files {1}", gvFiles.Rows.Count.ToString(), fileList.Count));

        Response.Clear();
        Response.BufferOutput = false;
        string zipName = String.Format("Zip_{0}.zip", DateTime.Now.ToString("yyyy-MMM-dd-HHmmss"));
        Response.ContentType = "application/zip";
        Response.AddHeader("content-disposition", "attachment; filename=" + zipName);
        zip.Save(Response.OutputStream);
        Response.End();
    }
}

private void LogFile(string filedetsils)
{
    string message = string.Format("Time: {0}", DateTime.Now.ToString("dd/MM/yyyy hh:mm:ss tt"));
    message += Environment.NewLine;
    message += "-----------------------------------------------------------";
    message += Environment.NewLine;
    message += string.Format("Message: {0}", filedetsils);
    message += Environment.NewLine;
    message += "-----------------------------------------------------------";
    message += Environment.NewLine;
    string path = Server.MapPath("~/Log/LogFile.txt");
    if (!(File.Exists(path)))
    {
        FileStream oFs = new FileStream(path, FileMode.Create);
        oFs.Close();
        oFs.Dispose();
    }
    using (StreamWriter writer = new StreamWriter(path, true))
    {
        writer.WriteLine(message);
        writer.Close();
    }
}

VB.Net

Protected Sub DownloadMultipleFileAsZip(ByVal sender As Object, ByVal e As EventArgs)
    Dim fileList As List(Of Files) = New List(Of Files)()
    For Each row As GridViewRow In gvFiles.Rows
        If (TryCast(row.FindControl("chkSelect"), CheckBox)).Checked Then
            Dim fileName As String = row.Cells(1).Text.Trim()
            Dim ftp As String = "ftp://yourserver.com/"
            Dim ftpFolder As String = "Uploads/"
            Try
                Dim request As WebClient = New WebClient()
                Dim url As String = ftp & ftpFolder & fileName
                request.Credentials = New NetworkCredential("Username", "Password")
                Dim bytes As Byte() = request.DownloadData(url)
                fileList.Add(New Files() With {.FileName = fileName, .Bytes = bytes})
            Catch ex As WebException
                Throw New Exception((TryCast(ex.Response, FtpWebResponse)).StatusDescription)
            End Try
        End If
    Next

    Using zip As ZipFile = New ZipFile()
        zip.AlternateEncodingUsage = ZipOption.AsNecessary
        zip.AddDirectoryByName("Files")
        For Each file As Files In fileList
            zip.AddEntry(file.FileName, file.Bytes)
        Next

        LogFile(String.Format("Total files {0} and downloaded files {1}", gvFiles.Rows.Count.ToString(), fileList.Count))

        Response.Clear()
        Response.BufferOutput = False
        Dim zipName As String = String.Format("Zip_{0}.zip", DateTime.Now.ToString("yyyy-MMM-dd-HHmmss"))
        Response.ContentType = "application/zip"
        Response.AddHeader("content-disposition", "attachment; filename=" & zipName)
        zip.Save(Response.OutputStream)
        Response.[End]()
    End Using
End Sub

Private Sub LogFile(ByVal filedetsils As String)
    Dim message As String = String.Format("Time: {0}", DateTime.Now.ToString("dd/MM/yyyy hh:mm:ss tt"))
    message += Environment.NewLine
    message += "-----------------------------------------------------------"
    message += Environment.NewLine
    message += String.Format("Message: {0}", filedetsils)
    message += Environment.NewLine
    message += "-----------------------------------------------------------"
    message += Environment.NewLine
    Dim path As String = Server.MapPath("~/Log/LogFile.txt")
    If Not (File.Exists(path)) Then
        Dim oFs As FileStream = New FileStream(path, FileMode.Create)
        oFs.Close()
        oFs.Dispose()
    End If

    Using writer As StreamWriter = New StreamWriter(path, True)
        writer.WriteLine(message)
        writer.Close()
    End Using
End Sub

Screenshot