Question

4^x.4²>1/16 resolva para mim pfv

Answer 1

Olá,

usando as propriedades EXPONENCIAIS, 

$a^{m}\cdot a^{n}=a^{m+n}\\\\ \dfrac{1}{a^m}=a^{-m}$

então podemos resolver esta desigualdade exponencial..

$4^x\cdot4^2\ \textgreater \ \dfrac{1}{16}\\\\ 4^{x+2}\ \textgreater \ \dfrac{1}{4^2}\\\\ \not4^{x+2}\ \textgreater \ \not4^{-2}\\\\ x+2\ \textgreater \ -2\\ x\ \textgreater \ -2-2\\\\ x\ \textgreater \ -4$

Sendo assim,

$\Large\boxed{\text{S}=\{x\in\mathbb{R}~|~x\ \textgreater \ -4\}}$