def _get_log_time_scale(units):
    """Retrieves the ``log10()`` of the scale factor for a given time unit.

    Args:
        units (str): String specifying the units
            (one of ``'fs'``, ``'ps'``, ``'ns'``, ``'us'``, ``'ms'``, ``'sec'``).

    Returns:
        The ``log10()`` of the scale factor for the time unit.
    """
    scale = {"fs": -15, "ps": -12, "ns": -9, "us": -6, "ms": -3, "sec": 0}

    units_lwr = units.lower()
    if units_lwr not in scale:
        raise ValueError(f"Invalid unit ({units}) provided")
    else:
        return scale[units_lwr]