✅ Após resolver equação exponencial, concluímos que seu conjunto solução é:
[tex]\Large\displaystyle\text{$\begin{gathered}\boxed{\boxed{\:\:\:\bf S = -1\:\:\:}}\end{gathered}$}[/tex]
Resolvendo equação exponencial:
[tex]\Large\displaystyle\text{$\begin{gathered} \Bigg(\frac{1}{4} \Bigg)^{x - 1} = 16^{x + 2}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} \Bigg(\frac{1}{2^{2}} \Bigg)^{x - 1} = 2^{4(x + 2)}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} 2^{-2(x - 1)} = 2^{4(x + 2)}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} 2^{-2x + 2} = 2^{4x + 8}\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} -2x + 2 = 4x + 8\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} -2x - 4x = 8 - 2\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} -6x = 6\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} x = - \frac{6}{6} \end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} x = -1\end{gathered}$}[/tex]
✅ Portanto, o conjunto solução é:
[tex]\Large\displaystyle\text{$\begin{gathered} S = \{-1\}\end{gathered}$}[/tex]
Saiba mais:
