extended phase space $$(d-3)M=(d-2)TS+(d-3)Q\Phi -2PV+2\left( \mathcal{A}_{1}\alpha +\mathcal{A}%
_{2}\alpha ^{2}\right) -\mathcal{B}\beta  \label{Smarr2}$$where $$\begin{aligned}
V &=&\frac{r_{+}^{n}}{n}, \\
\mathcal{A}_{1} &=&\frac{(n-1)k^{2}r_{+}^{n-4}}{16\pi }-\frac{%
(n-1)kTr_{+}^{n-3}}{2(n-3)}, \\
\mathcal{A}_{2} &=&\frac{(n-1)k^{3}r_{+}^{n-6}}{24\pi }-\frac{%
(n-1)k^{2}Tr_{+}^{n-5}}{2(n-5)}, \\
\left. \mathcal{B}\right\vert _{\text{ENED}}
&=&\frac{q(n-1)r_{+}\left(
L_{W+}\right) ^{\frac{3}{2}}F\left( [1],[\frac{5n-6}{2n-2}],\frac{L_{W+}}{%
2n-2}\right) }{8\pi n(3n-4)}-\frac{\beta r_{+}^{n}}{8\pi n}+\frac{q\beta
r_{+}^{n+1}\sqrt{L_{W+}}\left( 1-L_{W+}\right) }{8\pi n\left(
1+L_{W+}\right) }+\frac{2qr_{+}}{8\pi n\sqrt{L_{W+}}\left( 1+L_{W+}\right) },
\\
\left. \mathcal{B}\right\vert _{\text{LNED}} &=&\frac{\beta
r_{+}^{n}}{2\pi
n^{2}}\left[ -(n-1)\left( 1-\Gamma _{+}^{2}\right) F\left( \left[ \frac{1}{2}%
,\frac{n-2}{2n-2}\right] ,\left[ \frac{3n-4}{2n-2}\right] ,1-\Gamma
_{+}^{2}\right) +2n\ln \left( \frac{1+\Gamma _{+}}{2}\right) +(3n-2)\left(
1-\Gamma _{+}\right) \right] .\end{aligned}$$Regarding the mentioned argument and using Eqs. (\[P\]) and (\[T2\]), one can obtain the equation of state $P(V,T)$ to compare the black hole system with the Van der Waals fluid equation in ($n+1$)-dimensions [PVlovelock]{}.

 CLOSING REMARKS
================

In this paper we considered third order Lovelock gravity in the presence of exponential and logarithmic forms of NED models. Regardless of naked singularities, we obtained topological black hole solutions with two horizons or one (non-)extreme horizon. We found that replacing $\Lambda$ with an effective cosmological constant, $\Lambda_{eff}$, one may obtain asymptotically adS solutions. In other words, Lovelock gravity and also BI type NED models do not alter the asymptotical behavior of the solutions. We obtained thermodynamics and conserved quantities of the topological black holes and found that the Lovelock gravity 