Question

Qual o resultado da equação exponencial: (√2)^x = 64

Answer 1

$\\ \mathsf{(\sqrt{2})^x = 64} \\\\ \mathsf{\left ( 2^{\frac{1}{2}} \right )^x = 2^6} \\\\ \mathsf{2^{\frac{x}{2}} = 2^6} \\\\ \mathsf{\frac{x}{2} = 6} \\\\ \boxed{\mathsf{x = 12}}$

Answer 2

✅ Após resolver a equação exponencial, concluímos que seu conjunto solução é:

      $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf S = 12\:\:\:}}\end{gathered} }$

Resolvendo equação exponencial:

     $\Large\displaystyle\begin{gathered} (\sqrt{2})^{x} = 64\end{gathered}$

            $\Large\displaystyle\text{ \begin{gathered} 2^{\frac{x}{2} } = 2^{6}\end{gathered} }$

              $\Large\displaystyle\begin{gathered} \frac{x}{2} = 6\end{gathered}$

              $\Large\displaystyle\begin{gathered} x = 12\end{gathered}$

✅ Portanto, o conjunto solução é:

              $\Large\displaystyle\begin{gathered} S = \{12\}\end{gathered}$

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