Question

Qual o valor de x na igualdade



a) 4

b) 6

C) 8

d) 12​

Answer 1

Propriedade usada

$\sqrt[a]{b^c}=b^{\frac{c}{a}}$

Solução :

$\sqrt[16]{2^8}=\sqrt[x]{2^4}\\\\2^{\frac{8}{16}}=2^{\frac{4}{x}}\quad\mbox{se as bases sao iguais entao os expoentes tambem sao iguais, logo}\\\\\dfrac{8}{16}=\dfrac{4}{x}\\\\8x=4\cdot16\\\\x=\dfrac{64}{8} \\\\\boxed{\boxed{x=8}}$