def _log_removed_output(log_file, original, new, type_):
    """
    function writing the output of functions that remove datapoints to a log file.

    Parameters
    ----------
    log_file : str
        string containing the directory to the log file to be written out
    original : int
        original length of the dataset
    new : int
        length of the new dataset
    type_ : str
        'removed' or 'dropped'
    """
    log_file = open(log_file, 'a')
    log_file.write(str('\nOriginal dataset: ' + str(original) +
        ' datapoints; new dataset: ' + str(new) + ' datapoints' + str(
        original - new) + ' datapoints ', type_))
    log_file.close()
