This study focuses on developing and analysing a cosmological model based on the logarithmic \(f\left( Q \right)\) gravity framework, where the non-metricity scalar is denoted by \(Q\) . Our model assumes a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe containing an interacting mixture of Holographic Dark Energy (HDE) and a Domain Wall (DW) fluid. We employ a hybrid expansion law \(a\left( t \right) = \left( {\frac{t}{{t_{0} }}} \right)^{\alpha } e^{{\beta \left( {\frac{t}{{t_{0} }} - 1} \right)}}\) , to govern the cosmic dynamics, which naturally facilitates a shift from an initial, slowing expansion phase to the current period of acceleration. To assess the model’s versatility, we investigate three distinct HDE formulations prominent in the literature. The evolution of the deceleration parameter is examined, and the model's physical viability is assessed via a detailed analysis of the energy conditions for each fluid component, both of which are determined by solving the modified field equations for \(f\left( Q \right) = m + nlog\left( Q \right)\) . Our results demonstrate that the model successfully describes late-time cosmic acceleration. A comparative study of HDE models is also presented. Significantly, our analysis reveals a clear division of roles: the HDE component consistently violates the Strong Energy Condition, driving acceleration, while the domain wall component adheres to all energy conditions, behaving as a conventional matter source.
