Решите уравнение[latex] 7^{x+1} +3 * 7^{x}= 2^{x+5}+3* 2^{x} [/latex]

[latex]\displaystyle 7^{x+1}+3*7^x=2^{x+5}+3*2^x[/latex] [latex]\displaystyle 7*7^x+3*7^x=2^5*2^x+3*2^x 7^x(7+3)=2^x(32+3) 10*7^x=35*2^x [/latex] [latex]\displaystyle (\frac{7}{2})^x = \frac{35}{10} [/latex] [latex]\displaystyle (\frac{7}{2})^x= \frac{7}{2}[/latex] [latex]\displaystyle x=1[/latex] **************  Проверка [latex]\displaystyle 7^2+3*7^1=2^6+3*2^1 49+21=64+6 70=70[/latex]