In the last discussion, we saw that t\propto[H^{+}]^{-1}\iff\log t\propto-\log(H^{+}). This can be represented graphically by plotting our data (and regression line) on a log-log graph, which have axes both scaled logarithmically. Normally, an axis increases linearly, with the distance between each tick being constant, but a logarithmically scaled graph has a constant multiplier between adjacent tick on the axis:

Normal graph:

log-log graph:

As you can see, the original data on the "normal graph" is hard to make sense of because of the extreme values and non-linear relationship. The log-log graph is better because we can make better sense of our data. On the normal graph, the difference in H^+ between the last three points are indistinguishable, but we can still see trends in the logarithmically scaled data as H^+ gets very near zero.

Similarly, if we started with pH, a normal graph would yield an exponential relationship, so we prefer to plot our points on a semi-log graph, where only one of the axes is logarithmic (in this case t):

Normal graph:

semi-log graph:

Log models, scales and linearization