Question

LOG Raiz quadrada de 2  8 raiz quadrada de 2

Answer 1

$log_{(\sqrt{2})}(8\sqrt{2})=x$

Aplicando a definição de logaritmos:

$(\sqrt{2})^{x}=8\sqrt{2}\\\\\\\dfrac{(\sqrt{2})^{x}}{\sqrt{2}}=8\\\\\\(\sqrt{2})^{x-1}=8$

Transformando √2 e 8 em potências de 2:

$(2^{\frac{1}{2}})^{x-1}=2^{3}\\\\2^{\frac{x-1}{2}}=2^{3}$

Bases iguais, iguale os expoentes:

$\dfrac{x-1}{2}=3\\\\\\x-1=2\cdot3\\\\\\x-1=6\\\\\\x=6+1\\\\\\\boxed{\boxed{x=7}}$