  This paper is devoted to study the generalized second law of thermodynamics
in $f(T)$ gravity. We use quantum corrections such as power-law and logarithmic
corrected entropies to the horizon entropy along with Gibbs' equation in the
thermal equilibrium state. We derive $f(T)$ model by taking into account a
power-law scale factor through the first modified Friedmann equation which
obeys the condition for a realistic model. Two types of horizons, i.e., Hubble
and event horizons are used to check the validity of the generalized second law
of thermodynamics with corrected entropies. We conclude that this law holds
with a specific range of entropy parameter on both horizons in the case of
power-law corrected entropy, while it violates for all values of entropy
parameter on both horizons for logarithmic corrected entropy.
