  We propose a logarithmic parametrization form of energy density for the
scalar field dark energy in the framework of the standard theory of gravity,
which supports the necessary transition from the decelerated to the accelerated
behavior of the Universe. The model under consideration is constrained by
available 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 and
is consistent with recent observations. For the combined data-sets, the present
value of the deceleration parameter is calculated to be
$q_{0}=-0.43^{+0.06}_{-0.06}$. Furthermore, the analysis yields constraints on
both the parameter density value for matter and the present value of the Hubble
parameter, 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 the
results obtained from Planck 2018. Finally, the study investigates how the mass
of a black hole evolves over time in a Universe with both matter and dark
energy. It reveals that the black hole mass increases initially but stops
increasing as dark energy dominates.
