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While learning about acidic and basic buffer solutions we were told that they can resist pH change if we add small amounts of acid or base by neutralizing the $\ce{H+}$/$\ce{OH-}$ ions from the added acid or base. But I am confused about the fact that if we add a small amount of base to an acidic buffer then after neutralization of the excess $\ce{OH-}$ ions from the base by the $\ce{H+}$ ions from the buffer, shouldn't the concentration of $\ce{H+}$ ions in the solution decrease, thereby making the solution acidic and reducing the $\mathrm{pH}$. (vice-versa for the addition of acid to a basic buffer)

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    $\begingroup$ Buffers resisting pH change does not mean pH is constant. It means pH changes a lot less than without them being present. See the Henderson-Hasselbalch ( not -bach) equation on Libretexts or on Wikipedia and also buffer solution. It was question of 1-2 minutes of search and copy/paste. You may want to pay more attention to searching before asking. $\endgroup$ – Poutnik Feb 17 at 7:21
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While learning about acidic and basic buffer solutions we were told that they can resist pH change if we add small amounts of acid or base by neutralizing the $\ce{H+/OH−}$ ions from the added acid or base.

Yes, the pH changes less when you add small amounts of acid or base to a buffer, and more if you add it to pure water or an unbuffered aqueous solution.

But I am confused about the fact that if we add a small amount of base to an acidic buffer then after neutralization of the excess $\ce{OH−}$ ions from the base by the H+ ions from the buffer, shouldn't the concentration of $\ce{H+}$ ions in the solution decrease,

Yes, that is what happens. As a consequence, the weak acid/base reaction of the buffer substances is no longer at equilibrium, and there will be a net reaction to replenish some of the $\ce{H+}$ that was lost.

thereby making the solution acidic and reducing the pH. (vice-versa for the addition of acid to a basic buffer)

This is probably a typo. When you add a small amount of base, the pH would go up, buffered or not. In the presence of buffer, it goes up a little, and in the absence of buffer, a lot.

(vice-versa for the addition of acid to a basic buffer)

Buffers stabilize the pH near the $\mathrm{p}K_\mathrm{a}$ of the conjugate weak acid in "both directions", so even if the pH of a solution is slightly acidic, it is able to buffer against addition of acid or base.

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This is linked to the fact that in a weak acid-base pair, the respective concentrations are linked to each other through their ratio. We have

$$K_\mathrm{a} = \frac{[\ce{A-}][\ce{H3O+}]}{[\ce{AH}]},$$

therefore

$$\mathrm{pH} = \mathrm{p}K_\mathrm{a} + \log\frac{[\ce{A-}]}{[\ce{HA}]}.$$

In water, the reaction is written

$$\ce{AH + H2O -> A- + H3O+}$$

If we add a little strong acid, then we shift the equilibrium a little in the direction of formation of the acid but as the concentrations are related to each other by the $K_\mathrm{a},$ the consequence on the $\mathrm{pH}$ is attenuated.

For a strong acid, the addition of another strong acid contributes totally to the increase in $\mathrm{pH}$ because there is no balance that counterbalances the addition of the acid (as is the case for a weak acid).

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