3^(x+1) + 3^x = 324 <=> (3^x)*3 + 3^x = 324 <=> (3^x)( 3 + 1) = 324 <=> (3^x)*4 = 324 <=> 3^x = 81 <=> 3^x = 3^4 <=> x = 4.

[latex]3^{x+1}+3^x=324\\\\3\cdot3^x+3^x=324\\\\3^x\cdot(3+1)=324\\\\4\cdot3^x=324\ \ \ /:4\\\\3^x=81\\\\3^x=3^4\iff x=4[/latex]