Question

2.Daca 2ⁿ+2ⁿ+¹≤24,n€ℕ*, atunci aparține mulțimii:
a)n€{1,2,3};
b)n€{0,1,2,3};
c)n€{0,1,2};
d)n€{2,3};
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Answer 1

$2^n+2^{n+1}\leq 24\\2^n(1+2)\leq 24\\2^n\leq 8\\2^n\leq 2^3 \implies n\leq 3 \ (1)\\dar \ n \in\mathbb{N}^* \ (2)\\(1),(2)\implies n \in \{1,2,3\}$