Question

resolva a seguinte equação exponencial (1/4)^x-1=16^x+2

Answer 1

$( \frac{1}{4} )^{x-1}= 16^{x+2}$

$(4^{-1})^{x-1}=(4^2)^{x+2}$

$\not4^{-x+1}=\not4^{2x+4}$

$-x+1=2x+4\\-x-2x=4-1~~ (-1)\\x+2x=-4+1\\3x=-3\\x= \frac{-3}{3} \\x=-1$

Answer 2

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

          $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf S = -1\:\:\:}}\end{gathered} }$

Resolvendo equação exponencial:

        $\Large\displaystyle\begin{gathered} \Bigg(\frac{1}{4} \Bigg)^{x - 1} = 16^{x + 2}\end{gathered}$

       $\Large\displaystyle\text{ \begin{gathered} \Bigg(\frac{1}{2^{2}} \Bigg)^{x - 1} = 2^{4(x + 2)}\end{gathered} }$

       $\Large\displaystyle\begin{gathered} 2^{-2(x - 1)} = 2^{4(x + 2)}\end{gathered}$

         $\Large\displaystyle\begin{gathered} 2^{-2x + 2} = 2^{4x + 8}\end{gathered}$

     $\Large\displaystyle\begin{gathered} -2x + 2 = 4x + 8\end{gathered}$

  $\Large\displaystyle\begin{gathered} -2x - 4x = 8 - 2\end{gathered}$

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

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

                   $\Large\displaystyle\begin{gathered} x = -1\end{gathered}$

✅ Portanto, o conjunto solução é:

                  $\Large\displaystyle\begin{gathered} S = \{-1\}\end{gathered}$

Saiba mais:

1. https://brainly.com.br/tarefa/807335
2. https://brainly.com.br/tarefa/51195279
3. https://brainly.com.br/tarefa/1175592
4. https://brainly.com.br/tarefa/1242062
5. https://brainly.com.br/tarefa/658987
6. https://brainly.com.br/tarefa/830416
7. https://brainly.com.br/tarefa/1241810
8. https://brainly.com.br/tarefa/51246113
9. https://brainly.com.br/tarefa/1850200
10. https://brainly.com.br/tarefa/1784337
11. https://brainly.com.br/tarefa/219235