pH stands for "power of hydrogen".  pH is the negative logarithm
(base ten) of hydrogen ion concentration. The hydrogen ion
concentration is usually a very large numbers (in absolute value),
and would have to be given as something like, say, -0.000000023
Numbers like that are unwieldy, but their logarithms in base 10
are not. Then too, pH was first used in 1909.  Back then there were 
no calculators or computers and tedious calculations were done by 
hand using logarithms to base 10, so it made calculations easier.

[A similar use of logarithms is found in the study of sound intensity.
Look up "sound intensity" or "decibel".]

Edwin