[latex]3^{2x-1}+3^{2x}=108[/latex]

([latex] 3^{2x} +3* 3^{2x} -108*3[/latex] ) = [latex]0[/latex] [latex]3^{2x} + 3* 3^{2x} -324 = 0[/latex] Замена [latex] 3^{2x} =a[/latex] [latex] a^{2} +3 a^{2} =324[/latex] [latex] 4a^{2} =324[/latex] [latex] a^{2} =81[/latex] [latex] 3^{2x} =81= 3^{4} [/latex] [latex]x=2[/latex]