Question

3 la puterea 2n+3+ 9la puterea n+1=2916

Answer 1

${3}^{2n + 3} + {9}^{n + 1} = 2916 \\ {3}^{2n + 3} + ( {3}^{2} ) {}^{n + 1} = 2916 \\ {3}^{2n + 3} + {3}^{2n + 2} = 2916 \\ (3 + 1) \times {3}^{2n + 2} = 2916 \\ 4 \times {3}^{2n + 2} = 2916 \\ {3}^{2n + 2} = 729 \\ {3}^{2n + 2} = {3}^{6} \\ 2n + 2 = 6 \\ 2n = 4 \\ n = 2$