This paper presents a comparative analysis of four mathematical models (logarithmic, modified Gompertz, logistic, and Baranyi) for describing pH dynamics during ayran fermentation. Experimental data were obtained from laboratory fermentation runs with two functional additives at varying dosages (0–4% w/w). pH measurements were performed using a calibrated potentiometric pH meter  at 2-hour intervals (at 2, 4, 6, 8, and 10 hours) over a 10-hour fermentation period. The logarithmic model pH(t) = a – b·ln(t+1) – c·Dose showed highest accuracy: R²=0.9985, MAE=0.015, RMSE=0.018. The Baranyi model showed moderate performance, with R²=0.9856 for the control, 0.9717 for Additive 1, and 0.9928 for Additive 2. The Gompertz and logistic models showed poor performance, with highly negative R² values, including −180.5 (Gompertz) and −55.8 (logistic) for the control group, indicating a severe mismatch with the experimental data. The inverse problem for target pH=4.30±0.05 is solved analytically. One‑way ANOVA confirmed a statistically significant effect of additive type on final pH (F(2,3)=25.00, p=0.013) and fermentation time (F(2,3)=13.69, p=0.031). Post‑hoc Tukey HSD analysis revealed that both additives significantly altered acidification kinetics compared to the control (p<0.05). The inverse problem of predicting the time required to reach the target pH = 4.30±0.05 is solved analytically using the logarithmic model. The proposed dose‑dependent logarithmic model provides a robust, computationally efficient tool for quantitative analysis of ayran fermentation kinetics and can be applied to other low‑viscosity fermented dairy systems, enabling formulation optimization and process control without specialized hardware.