\text{-2}\\ -\text{log}_{2}\text{(2}^{x}-1\text{+2}^{x}-2)>-2\\ \text{log}_{2}\left( 2^{x+1}-3\right) <2\text{log}_{2}2\\ 2^{x+1}-3<4\\ 2^{x+1}-2^{1}-2^{0}<2^{2}\\ x+1-1-0<2.\\ x<2. \end{array}" alt="\begin{array}{l} \text{log}_{2}\left( 2^{x}-1\right) \times \text{log}_{2^{-1}}\left( 2x-2\right) >\text{-2}\\ -\text{log}_{2}\text{(2}^{x}-1\text{+2}^{x}-2)>-2\\ \text{log}_{2}\left( 2^{x+1}-3\right) <2\text{log}_{2}2\\ 2^{x+1}-3<4\\ 2^{x+1}-2^{1}-2^{0}<2^{2}\\ x+1-1-0<2.\\ x<2. \end{array}" align="absmiddle" class="latex-formula">