Question

(UEPB PB) O valor de x na inequação exponencial (5/2)^x > 0,16 é dado por: a) x>-2 b)c<-2 c)x>2 d)x<2 e)x<1/2

Answer 1

$(\dfrac{5}{2})^{x} \ \textgreater \ 0,16 \\ \\ (\dfrac{5}{2})^{x} \ \textgreater \ \dfrac{16:4}{100:4} = \dfrac{4}{25} \\ \\ (\dfrac{5}{2})^{x} \ \textgreater \ (\dfrac{5^2}{2^2})^{-1} \\ \\ (\dfrac{5}{2})^{x} \ \textgreater \ [ (\dfrac{5}{2})^2]^{-1} \\ \\ (\dfrac{5}{2})^{x} \ \textgreater \ (\dfrac{5}{2})^{-2} \Longrightarrow \ pot\^encias \ de \ mesma \ base \\ \\ \ A \ base \ \dfrac{5}{2} \ \textgreater \ 1 \Longrightarrow a \ desigualdade \ se \ mantem \\ \\ \therefore \ x \ \textgreater \ -2 \ \Longrightarrow \ Alternativa \ A$

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Obrigado pela oportunidade 
Boa sorte, bons estudos!
SSRC - ♑ - 2015 
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