Question

Raiz de 2 elevado a x é igual a 8 raiz de 2

Answer 1

Explicação passo a passo:

${(\sqrt{2})}^x=8\sqrt{2}\\\\\dfrac{{(\sqrt{2})}^x}{\sqrt{2}}=8\\\\{(\sqrt{2})}^{x - 1}=8\\\\{(2^{\frac{1}{2}})}^{x - 1}=8\\\\2^{\frac{x - 1}{2}}=8\\\\2^{\frac{x - 1}{2}}=2^3\\\\\dfrac{x - 1}{2}=3\Longrightarrow x - 1=2\cdot 3=6\\\\x=6+1\Longrightarrow x=7$