Question

Resolva as inequações exponenciais abaixo :

b) ( 5 / 2 )^{x + 2} > 0,4

d) ( 1 / 5 )ˣ > 125

Answer 1

Caso esteja pelo app, e tenha problemas para visualizar esta resposta, experimente abrir pelo navegador https://brainly.com.br/tarefa/41346977

                                             

Propriedade das funções exponenciais

$\large\boxed{\begin{array}{l}\rm \checkmark se~ a~base~\acute e~maior~que~1~a~desigualdade~se~mant\acute em .\\\checkmark~\rm se~a~base~est\acute a~entre~0~e~1~a~desigualdade~se~inverte\end{array}}$

$\large\boxed{\begin{array}{l}\tt b)\\\sf 0,4=\dfrac{4\div2}{10\div2}=\dfrac{2}{5}\\\sf\bigg(\dfrac{5}{2}\bigg)^{x+2}>0,4\\\sf\bigg(\dfrac{5}{2}\bigg)^{x+2}>\dfrac{2}{5}\\\sf\bigg(\dfrac{5}{2}\bigg)^{x+2}>\bigg(\dfrac{5}{2}\bigg)^{-1}\\\sf x+2>-1\\\sf x>-2-1\\\sf x>-3\\\sf S=\{x\in\mathbb{R}/x>-3\}\end{array}}$

$\Large\boxed{\begin{array}{l}\tt d)~\sf\bigg(\dfrac{1}{5}\bigg)^x>125\\\sf \bigg(\dfrac{1}{5}\bigg)^x>\bigg(\dfrac{1}{5}\bigg)^{-3}\\\sf x<-3\\\sf S=\{x\in\mathbb{R}/x<-3\}\end{array}}$