[tex]49^{\Big{\text{x}}}-8\cdot 7^{\Big{\text{x}}}+7 = 0 \Rightarrow \\ \Rightarrow \Big(7^{\Big2}\Big)^{\Big{\text{x}}} - 8\cdot 7^{\Big{\text{x}}}+7 = 0\Rightarrow \\ \Rightarrow 7^{\Big{2\cdot\text{x}}}-8\cdot 7^{\Big{\text{x}}}+7=0 \Rightarrow \\ \Rightarrow \Big(7^{\Big{\text{x}}}\Big)^\big2-8\cdot 7^{\Big{\text{x}}}+7 = 0\\ \\ $Notam $ 7^{\Big{\text{x}}}= t,\quad t>0:\\ \\ \Rightarrow t^2-8t+7=0 \Rightarrow \\ \Rightarrow t^2-t-7t+7 = 0 \Rightarrow \\ [/tex]
[tex]\Rightarrow t(t-1)-7(t-1) = 0 \Rightarrow \\ \Rightarrow (t-1)(t-7) = 0 \\ \\ \bullet $ $ t = 1 \Rightarrow 7^{\Big{\text{x}}}=1 \Rightarrow \text{x} =0\\ \bullet $ $t = 7 \Rightarrow 7^{\Big{\text{x}}} = 7 \Rightarrow \text{x} = 1 \\ \\ \Rightarrow S = \Big\{0;1\Big\}[/tex]
