![image](https://tex.z-dn.net/?f=2%5E%7B2x%7D-6%5Ccdot+2%5E%7Bx%7D%2B8%3D0%5C%5C%5C%5CZamena%3A%5C%3B+t%3D2%5E%7Bx%7D%3E0%2C%5C%3B+%5C%3B+2%5E%7B2x%7D%3D%282%5E%7Bx%7D%29%5E2%3Dt%5E2%5C%5C%5C%5Ct%5E2-6t%2B8%3D0%5C%5C%5C%5Ct_1%3D2%2C%5C%3B+t_2%3D4%5C%3B+%28teor.%5C%3B+Vieta%29%5C%5C%5C%5C1%29%5C%3B+%5C%3B+2%5E%7Bx%7D%3D2%2C%5C%3B+x%3D1%5C%5C%5C%5C2%29%5C%3B+%5C%3B+2%5E%7Bx%7D%3D4.%5C%3B+%5C%3B+2%5E%7Bx%7D%3D2%5E2%2C%5C%3B+%5C%3B+x%3D2)
0,\; \; 2^{2x}=(2^{x})^2=t^2\\\\t^2-6t+8=0\\\\t_1=2,\; t_2=4\; (teor.\; Vieta)\\\\1)\; \; 2^{x}=2,\; x=1\\\\2)\; \; 2^{x}=4.\; \; 2^{x}=2^2,\; \; x=2" alt="2^{2x}-6\cdot 2^{x}+8=0\\\\Zamena:\; t=2^{x}>0,\; \; 2^{2x}=(2^{x})^2=t^2\\\\t^2-6t+8=0\\\\t_1=2,\; t_2=4\; (teor.\; Vieta)\\\\1)\; \; 2^{x}=2,\; x=1\\\\2)\; \; 2^{x}=4.\; \; 2^{x}=2^2,\; \; x=2" align="absmiddle" class="latex-formula">
Ответ: 1 и 2.