Question

(UMC-SP) O valor de n natural tal que
${2}^{n} = 4 \times \sqrt[5]{ {8}^{n} }$
é:
a)12
b)10
c)8
d)4
e)5​

Answer 1

Resposta: e) 5

$2^{n}=2^{2}*8^{\frac{n}{5}}\\2^{n}=2^{2}*(2^{3})^{\frac{n}{5}}\\2^{n}=2^{2}*2^{\frac{3*n}{5}}\\2^{n}=2^{2}*2^{\frac{3n}{5}}\\n=2+\frac{3n}{5}\\5n=10+3n\\5n-3n=10\\2n=10\\n=\frac{10}{2}\\\boxed{n=5}$

Alternativa E) 5

Explicação passo-a-passo:

Provando;

$2^{5}=4*\sqrt[5]{8^{5}}\\2*2*2*2*2=4*8\\2*4*4=32\\2*16=32$