Question

Determina numarul natural n , astfel incat 3 la puterea n + 4×3 la puterea n+1 + 3 la puterea n+2=594

Answer 1

${3}^{n} + 4 \times {3}^{n + 1} + {3}^{n + 2} = 594 \\ {3}^{n} (1 + 4 \times 3 + {3}^{2} ) = 594 \\ {3}^{n} \times 22 = 594 \\ {3}^{n} = 27 \\ n = \sqrt[3]{27} \\ n = 3$
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