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We propose a logarithmic parametrization form of energy density for thescalar field dark energy in the framework of the standard theory of gravity,which supports the necessary transition from the decelerated to the acceleratedbehavior of the Universe. The model under consideration is constrained byavailable observational data, including cosmic chronometers data-sets (CC),Baryonic Acoustic Oscillation (BAO) data-sets, and Supernovae (SN) data-sets,consisting of only two parameters $\alpha$ and $\beta$. The combined$CC$+$BAO$+$SN$ data-sets yields a transition redshift of$z_{tr}=0.79^{+0.02}_{-0.02}$, where the model exhibits signature-flipping andis consistent with recent observations. For the combined data-sets, the presentvalue of the deceleration parameter is calculated to be$q_{0}=-0.43^{+0.06}_{-0.06}$. Furthermore, the analysis yields constraints onboth the parameter density value for matter and the present value of the Hubbleparameter, with values of $\Omega_{m0}=0.25849^{+0.00026}_{-0.00025}$ and$H_{0}=67.79_{-0.59}^{+0.59}$ $km/s/Mpc$, respectively, consistent with theresults obtained from Planck 2018. Finally, the study investigates how the massof a black hole evolves over time in a Universe with both matter and darkenergy. It reveals that the black hole mass increases initially but stopsincreasing as dark energy dominates.

Observational constraints on a logarithmic scalar field dark energy model and black hole mass evolution in the Universe