I've seen the plots and they don't look drastically different. Why do this?
Why use a logarithmic scale when plotting pharmacodynamics/kinetics?
There could be several reasons for this. You mention in the comments that your plot of interest is the concentration-time profile. As you can see, plotting the logarithm of concentration vs time yields a very different plot for a drug administered intravenously.
The reason this is done is because the two plots yield different information. The slope of the log(C) vs t plot actually yields the elimination constant, Ke. The logarithmic plot can also be used to assess if the drug is distributed into one or more compartments. If the drug is distributed into two or more compartments, the initial slope would be different than the remainder (but this is not pictured here).
In terms of pharmacodynamics, its often useful to assess how a 10- or 100- fold increase in concentration affects the effect.