scales give the logarithm
of a quantity instead of the quantity itself. This is often done if the underlying quantity can take on a huge range of values; the logarithm reduces this to a more manageable range. Some of our senses operate in a logarithmic fashion (doubling the input strength adds a constant to the subjective signal strength), which makes logarithmic scales for these input quantities especially appropriate. In particular our sense of "audition", i.e., hearing, is naturally designed to perceive equal ratios of frequencies as equal differences in pitch.
Logarithmic scales are either defined for ratios of the underlying quantity, or one has to agree to measure the quantity in fixed units. Deviating from these units means that the logarithmic measure will change by an additive constant. The base of the logarithm also has to be specified.
In the first five examples small values (or ratios) of the underlying quantity will correspond to negative values of the logarithmic measure.
In the last two examples large values (or ratios) of the underlying quantity will correspond to negative values of the logarithmic measure, because of reversal of the scale by a minus sign in the definition.