Copper reduces NO$_3^-$ into NO and NO$_2$ depending upon the concentration of HNO$_3$ in solution. (Assuming fixed [Cu$^{2+}$] and $P_{NO}=P_{NO_2}$), the HNO$_3$ concentration at which the thermodynamic tendency for reduction of NO$_3^-$ into NO and NO$_2$ by copper is same is $10^x$ M. The value of 2x is ________. (Rounded-off to the nearest integer)
[Given, E$^\circ_{Cu^{2+}/Cu}$=0.34 V, E$^\circ_{NO_3^-/NO}$=0.96 V, E$^\circ_{NO_3^-/NO_2}$=0.79 V and at 298 K, $\frac{RT}{F}$(2.303)=0.059]