Question

Sobre equação exponencial:


$3^{x+4}$ = $\frac{1}{243}$

Answer 1

$\sf3^{x+4}=\dfrac{1}{243}$

$\begin{array}{r|l}\sf243&\sf3\\\sf81&\sf3\\\sf27&\sf3\\\sf9&\sf3\\\sf3&\sf3\\\sf1&\overline{\sf243=3^5}\end{array}$

$\sf3^{x+4}=\dfrac{1}{3^5}$

$\sf3^{x+4}=3^{-5}$

$\sf x+4=-5$

$\sf x=-5-4$

$\boxed{\boxed{\sf x=-9}}$

Answer 2

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

   $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf S = \{-9\}\:\:\:}}\end{gathered} }$  

Resolvendo a equação exponencial:

       $\Large\displaystyle\begin{gathered}\tt 3^{x + 4} = \frac{1}{243}\end{gathered}$

       $\Large\displaystyle\text{ \begin{gathered}\tt 3^{x + 4} = \frac{1}{3^{5}}\end{gathered} }$

      $\Large\displaystyle\begin{gathered}\tt {\!\diagup\!\!\!\!3}^{x + 4} = {\!\diagup\!\!\!\!3}^{-5}\end{gathered}$

     $\Large\displaystyle\begin{gathered}\tt x + 4 = -5\end{gathered}$

              $\Large\displaystyle\begin{gathered}\tt x = -5 - 4\end{gathered}$

              $\Large\displaystyle\begin{gathered}\tt x = -9\end{gathered}$

✅ Portanto, o conjunto solução é:

              $\Large\displaystyle\begin{gathered}\tt S = \{-9\}\end{gathered}$

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