Question

resolva a inequação exponencial (32)^-x<1/2

Answer 1

Dada a inequação exponencial:

$\mathsf{32^{-x}\ \textless \ \dfrac{1}{2}}$

= = = = =

Transformando as bases para um numero em comum:

$\mathsf{\left(2^5\right)^{-x}\ \textless \ 2^{-1}}\\\\\mathsf{2^{-5x}\ \textless \ 2^{-1}}\\\\\mathsf{-5x\ \textless \ -1}\\\\\mathsf{5x\ \textgreater \ 1}\\\\\mathsf{x\ \textgreater \ \dfrac{1}{5}}$

= = = = =

$\boxed{\mathsf{Resposta:\:S=\left\{x\in \mathbb{R}\:,\:x\ \textgreater \ \dfrac{1}{5}\right\}}}\: \: \checkmark$