Question

Rezolvati ecuatia 3 la puterea x+3 + 3 la puterea x+2 - 3 la puterea x = 315

Answer 1

     
$3^{x+3} + 3^{x+2} -3^{x} =315 \\ 3^{x+3} + 3^{x+2} -3^{x} =35\cdot3^2 \\ 3^x\cdot(3^{3} + 3^{2} -3^{0}) =35\cdot3^2 \\ 3^x\cdot(27 + 9 -1) =35\cdot3^2 \\ 3^x\cdot(35) =35\cdot3^2 \\ 35\cdot3^x =35\cdot3^2 \;\;\;\;\; | : 35 \\ 3^x=3^2 \\ =\ \textgreater \ \;\;\;\; x = \boxed{2}$