Question

como ser resolver esta equaçoes exponencias 3.4x+1=96

Answer 1

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

 $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf S = \Bigg\{\frac{3}{2} \Bigg\}\:\:\:}}\end{gathered} }$

Resolvendo equação exponencial:

   $\Large\displaystyle\begin{gathered}3\cdot4^{x + 1} = 96 \end{gathered}$

         $\Large\displaystyle\begin{gathered}4^{x + 1} = \frac{96}{3} \end{gathered}$

         $\Large\displaystyle\begin{gathered}4^{x + 1} = 32 \end{gathered}$

    $\Large\displaystyle\begin{gathered}(2^{2})^{x + 1} = 2^{5} \end{gathered}$

        $\Large\displaystyle\begin{gathered}2^{2x + 2} = 2^{5} \end{gathered}$

     $\Large\displaystyle\begin{gathered}2x + 2 = 5 \end{gathered}$

              $\Large\displaystyle\begin{gathered}2x = 5 - 2 \end{gathered}$

              $\Large\displaystyle\begin{gathered}2x = 3 \end{gathered}$

                $\Large\displaystyle\begin{gathered}x = \frac{3}{2} \end{gathered}$

✅ Portanto, o conjunto solução da equação é:

              $\Large\displaystyle\text{ \begin{gathered}S = \Bigg\{\frac{3}{2} \Bigg\} \end{gathered} }$

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Answer 2

Explicação passo-a-passo:

$3 \times 4 {}^{x + 1} = 96$

$3 \times 4 {}^{x + 1} = 96( \div 3)$

$4 {}^{x + 1} = 32$

$2 {}^{2x + 2} = 2 {}^{5}$

$2x + 2 = 5$

$2x = 5 - 2$

$2x = 3$

x=>3/2