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They both react with phenol. KOH is actually a slightly stronger base than NaOH.

At low concentrations, like less than 0.1M, both NaOH and KOH are essentially 100% dissociated. However, at higher concentrations, a little more of the KOH is dissociated. The point is, both bases will remove virtually all of the H+ from phenol. You received some incorrect information.

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