Send via e-mail

final Intent intent = new Intent(Intent.ACTION_SEND);
intent.setType("message/rfc822");
intent.putExtra(Intent.EXTRA_EMAIL, "some@mail.ru");
intent.putExtra(Intent.EXTRA_SUBJECT, "subject");
intent.putExtra(Intent.EXTRA_TEXT, "mail body");

final File logFile = ...

if (null != logFile && logFile.exists())
{
   intent.putExtra(Intent.EXTRA_STREAM, Uri.fromFile(logFile));
}

context.startActivity(Intent.createChooser(intent, null)); // context - android.contetn.Context