Why is concentration used as an input for pH calculations?

[zyj]

This is something I've been wondering for a while, but I thought that the inputs for things like ln(x), e^(x), sin(x), etc. had to be unitless. Then how come concentration, which has units of moles per volume (or I guess just per volume, since moles are just a number? I've never been sure about that...) is used as an input for log(x) to find pH, pOH, pK_a, etc.?

 

[Jorriss]

I've never thought about that myself.

I would suspect it is because formula pH is defined as, pH=-log(a) where a is the activity of the hydrogen ion and activity is dimensionless.