[tex]\displaystyle\bf\\2^{2013}<2x-2<2^{2015}~~~unde~~x\in N\\\\2^{2013}+1\leq 2x-2\leq 2^{2015}-1~~~\Big|+2\\\\2^{2013}+1+2\leq 2x\leq 2^{2015}-1+2\\\\2^{2013}+3\leq 2x\leq 2^{2015}+1~~~\Big|:2\\\\\frac{2^{2013}+3}{2}\leq x\leq\frac{2^{2015}+1}{2}\\\\\\\frac{2^{2013}}{2}+\frac{3}{2}\leq x\leq\frac{2^{2015}}{2}+\frac{1}{2}\\\\\\2^{2013-1}+1,5\leq x\leq2^{2015-1}+0,5\\\\\\2^{2012}+1,5\leq x\leq2^{2014}+0,5~~~,dar~x\in N\\\\\\\implies\boxed{\bf2^{2012}+2\leq x\leq2^{2014}}[/tex]
