Question

DAU COROANA!!!URGENT 3+3la puterea 2+3 la puterea 3+...+ 3la puterea x=120

Answer 1

   
[tex]\displaystyle \\ 3+3^2+3^3+\cdots + 3^x = 120 \\ \\ \frac{3^{x+1}-1}{3-1}-1 = 120 \\ \\ \frac{3^{x+1}-1}{2} = 120 +1\\ \\ \frac{3^{x+1}-1}{2} = 121\\ \\ 3^{x+1}-1 = 121 \cdot 2 \\ \\ 3^{x+1}-1 = 242 \\ \\ 3^{x+1} = 242 +1 \\ \\ 3^{x+1} = 243 \\ \\ 3^{x+1} = 3^5 \\ \\ x+1 = 5 \\ \\ x = 5-1 = \boxed{4} \\ \\ \texttt{Verificare:} \\ \\ 3+3^2+3^3+ 3^4 = 3+9+27+81=12+27+81=39+81=120~ok! [/tex]