3^{x+2} * 9^{3x-1} = 27^{x+4} \\\\ 3^{x}\cdot 3^2 \cdot 3^{2(3x-1)}=3^{3(x+4)} \\\\ 3^x \cdot 3^2 \cdot 3^{6x} \cdot 3^{-2}=3^{3x+12} \\\\ 3^{x+6x} \cdot 3^{2-2}=3^{3x+12} \\\\ 3^{7x} \cdot 3^0=3^{3x+12} \ , \ (3^0=1)\\\\ 3^{7x} = 3^{3x+12}\\\\ 7x=3x+12 \ |-3x \\\\ 4x =12 \ |:4 \\\\ x=3