  In the present work, we report a comprehensive shell-model study of the $\log
ft$ values for the forbidden $\beta^-$ decay transitions in the north-east
region of $^{208}$Pb. For this we have considered $^{210-215}$Pb $\rightarrow$
$^{210-215}$Bi and $^{210-215}$Bi $\rightarrow$ $^{210-215}$Po transitions. We
have performed shell-model calculation using KHPE interaction in valence shell
82-126 for protons and 126-184 for neutrons without any truncation. We have
also calculated half-lives and Q-values for the concerned nuclei. Recently
several $\log ft$ values are observed corresponding to $\beta^-$ decay from
(8$^-$) isomeric state of $^{214}$Bi$^m$ at CERN-ISOLDE facility [Phys. Rev. C
{\bf 104}, 054301 (2021)], and for the first time we have reported shell-model
results for these transitions.
