Решите уравнение: [latex]3^2^x-2*3^2^x^-^1-2*3^2^x^-^2=1[/latex]

[latex]\displaystyle 3^{2x}-2*3^{2x-1}-2*3^{2x-2}=1[/latex] [latex]\displaystyle 3^{2x}-2* \frac{3^{2x}}{3}-2* \frac{3^{2x}}{3^2}=1 [/latex] [latex]3^{2x}=t[/latex] [latex]\displaystyle t- \frac{2t}{3}- \frac{2t}{9}=1 [/latex] [latex]\displaystyle \frac{9t-6t-2t}{9}= \frac{9}{9} [/latex] [latex]\displaystyle 9t-6t-2t=9 t=9[/latex] [latex]\displaystyle 3^{2x}=9 3^{2x}=3^2 2x=2 x=1[/latex] Ответ х=1