Question

Determine o valor de x na equação exponencial 10^x-3 = 1/100

Answer 1

$10^{x-3}= \frac{1}{100}$

$10^{ ^{x-3} }=100^-^1$

$10^{x-3}=( 10^{2})^-^1$

$10^{x-3}= 10^{-2}$ ---bases iguais ,iguala os expoentes

x-3 = -2 --> x = -2 +3 --> x = 1

Answer 2

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

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

Resolvendo equação exponencial:

        $\Large\displaystyle\begin{gathered} 10^{x - 3} = \frac{1}{100} \end{gathered}$

        $\Large\displaystyle\text{ \begin{gathered} 10^{x - 3} = \frac{1}{10^{2}} \end{gathered} }$

        $\Large\displaystyle\begin{gathered} 10^{x - 3} = 10^{-2}\end{gathered}$

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

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

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

✅ Portanto, o conjunto solução da equação é:

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

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