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In this paper, we find the solutions of quartic quasitopological black holesand branes coupled to logarithmic and exponential forms of nonlinearelectrodynamics. These solutions have an essential singularity at $r=0$.Depending on the value of charge parameter $q$, we have an extreme blackhole/brane, a black hole/brane with two horizons or a naked singularity. Forsmall values of parameter $q$, the solutions lead to a black hole/brane withtwo horizons. The values of the horizons are independent of the values ofquasitopological parameters and depend only on the values of $q$, dimensions$n$, nonlinear parameter $\beta$ and mass parameter. Also, the solutions arenot thermally stable for dS and flat spacetimes. However, AdS solutions arestable for $r_{+}>{r_{+}}_{\rm{ext}}$ which the temperature is zero for$r_{+}={r_{+}}_{\rm{ext}}$. The value of ${r_{+}}_{\rm{ext}}$ also depends onthe values of parameters $q$, $\beta$, $n$ and $m$. As the value of${r_{+}}_{\rm{ext}}$ decreases, the region of stability becomes larger. We alsouse HPEM metric to probe GTD formalism for our solutions. This metric issuccessful to predict the divergences of the scalar curvature exactly at thephase transition points. For large values of parameter $\Xi$, the blackhole/brane has a transition to a stable state and stays stable.

Physical and thermodynamic properties of quartic quasitopological black holes and rotating black branes with nonlinear source