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The negative logarithm of the acid dissociation constant is the definition.
I think you are referring to buffers. At the point of half neutralisation, the acid and its conjugate base are at equal concentrations
Ka= [H+][A-]/[HA]
But when [HA]=[A-] half way through the reacion, this cancels down to Ka=[H+]
=> pKa=pH
Ka= [H+][A-]/[HA]
But when [HA]=[A-] half way through the reacion, this cancels down to Ka=[H+]
=> pKa=pH
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