Question

Se $2^{14}$+$2^{14}$+$2^{14}$+$2^{14}$=$2^{m}$, então qual é o valor de m?

(a)16
(b)15
(c)14
(d)13

Answer 1

$2^{14}+2^{14}+2^{14}+2^{14}=2^{\text m} \\\\ \text{somando os semelhantes : } \\\\ 4.\text 2^{14} = 2^{\text m} \\\\ 2^2.2^{14}=2^{\text m} \\\\ 2^{14+2} = 2^{\text m} \\\\ 2^{16}=2^{\text m } \\\\ \underline{\text{aplicando log dos dois lados : }} \\\\ \text{log }2^{16}=\text{log } 2^{\text m}\\\\ 16.\text{log 2} = \text m.\text{log 2} \\\\ \huge\boxed{\text m = 16 }\checkmark$

letra a