  The Hankel and Toeplitz determinants $H_{2,1}(F_{f^{-1}}/2)$ and
$T_{2,1}(F_{f^{-1}}/2)$ are defined as: \begin{align*}
  H_{2,1}(F_{f^{-1}}/2):= \begin{vmatrix}
  \Gamma_1 & \Gamma_2
  \Gamma_2 & \Gamma_3
  \end{vmatrix}
  \;\;\mbox{and} \;\;
  T_{2,1}(F_{f^{-1}}/2):= \begin{vmatrix}
  \Gamma_1 & \Gamma_2
  \Gamma_2 & \Gamma_1
  \end{vmatrix} \end{align*} where $\Gamma_1, \Gamma_2,$ and $\Gamma_3$ are the
first, second and third logarithmic coefficients of inverse functions belonging
to the class $\mathcal{S}$ of normalized univalent functions. In this article,
we establish sharp inequalities $|H_{2,1}(F_{f^{-1}}/2)|\leq 1/4$,
$|H_{2,1}(F_{f^{-1}}/2)| \leq 1/36$, $|T_{2,1}(F_{f^{-1}}/2)|\leq 5/16$ and
$|T_{2,1}(F_{f^{-1}}/2)|\leq 145/2304$ for the logarithmic coefficients of
inverse functions for the classes starlike functions and convex functions with
respect to symmetric points. In addition, our findings are substantiated
further through the incorporation of illustrative examples, which support the
strict inequality and lend credence to our conclusions.
