def lower_transform(mean, bound, logbase):
    """ Log transformation scaling.


    Examples
    --------
    Untransformed data looks as so:

        Yupper = Ymean + bound
        Ylower = Ymean - bound

    We want log(bounds)
        ie.
            log(Yupper) - log(Ymean)
            log(Ylower) + log(Ymean)

    so log(bound) = log(1 + bound/Ymean)
       log(bound) = log(1 - bound/Ymean)
    """
    return abs(logbase(mean / (mean - bound)))
