Question

Se 3^x = 2 para algum x ∈ R, qual é o valor de 3^−x/2 .

Answer 1

Olá Etherious.


Organizando e resolvendo a equação exponencial:


$\mathsf{3^x=2}\\\\\\\mathsf{3^{-\frac{x}{2}}~\Rightarrow~(3^x)^{-\frac{1}{2}}~\Rightarrow~(2)^{-\frac{1}{2}}~\Rightarrow~\boxed{\mathsf{\dfrac{1}{2^{\frac{1}{2}}}}}}~~~~ou~~~~~\boxed{\mathsf{\dfrac{1}{\sqrt{2}}}}$

Racionalizando:

$\mathsf{\dfrac{1}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}=\boxed{\mathsf{\dfrac{\sqrt{2}}{2}}}}$


Dúvidas? comente.