n∈N then the statement 8n+16≤2^n is true for

Correct answer: (C) n=6. Given that, 8n+16≤2^n ⇒2^3n+2≤2^n For n=6 2^3n+2=2^36+2=2^3·2^3=2^6 Hence, 8n+16≤2^n is true for n=6.

Q44 / 160 · AP EAMCET 2021 (19 Aug Shift 1) · Mathematics

$n \in N$ then the statement $8 n + 16 \leq 2^{n}$ is true for

Given that, $8 n + 16 \leq 2^{n}$

$\Rightarrow 2^{3} (n + 2) \leq 2^{n}$

For $n = 6$

$2^{3} (n + 2) = 2^{3} (6 + 2) = 2^{3} \cdot 2^{3} = 2^{6}$

Hence, $8 n + 16 \leq 2^{n}$ is true for $n = 6$ .

Hence, the correct answer is option: 'C'.