Adding hydrogen ion concentration while calculating pH

I have just started learning how to calculate pH and I have noticed that adding [$\ce{H+}$] makes a negligible difference in few cases whereas in other cases it makes a major change in the final value. Why is that?




pH is calculated by a logarithmic formula given by: 


$$\text{pH}=-\log{\ce{[H+]}}$$ 


Lets say, the initial hydrogen ion concentration is $\ce{[H+]\_0}$, and change in concentration is $d\ce{[H+]}$. The change in pH would be:


$$d\text{pH}=-\log{(\ce{[H+]\_0}+d\ce{[H+]})}$$


This can otherwise be written as:


$$d\text{pH}=-\log{\ce{[H+]\_0}}×\frac{d\ce{[H+]}}{\ce{[H+]\_0}}$$


You can see that the change in pH depends on the initial hydrogen ion concentration. It's in fact **inversely proportional to the initial concentration**. Adding a drop of concentrated acid to a base would give a much bigger change in pH compared to adding a drop to pure water, which in turn is bigger compared to adding a drop to an acid. 


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