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The Hankel determinant $H_{2,1}(F_{f^{-1}}/2)$ of logarithmic coefficients isdefined as: \begin{align*} H_{2,1}(F_{f^{-1}}/2):= \begin{vmatrix} \Gamma_1 &\Gamma_2 \Gamma_2 & \Gamma_3 \end{vmatrix}=\Gamma_1\Gamma_3-\Gamma^2_2,\end{align*} where $\Gamma_1, \Gamma_2,$ and $\Gamma_3$ are the first, secondand third logarithmic coefficients of inverse functions belonging to the class$\mathcal{S}$ of normalized univalent functions. In this article, we establishsharp inequalities $|H_{2,1}(F_{f^{-1}}/2)|\leq 19/288$,$|H_{2,1}(F_{f^{-1}}/2)| \leq 1/144$, and $|H_{2,1}(F_{f^{-1}}/2)| \leq 1/36$for the logarithmic coefficients of inverse functions, considering starlike andconvex functions, as well as functions with bounded turning of order $1/2$,respectively.

Second Hankel determinant of logarithmic coefficients of inverse functions in certain classes of univalent functions