Question

Resolva as inequaçoes:

A) $\frac{1}{81})^x \geq 9^x^+^3$

B) $\sqrt{5}^x\ \textless \ 125$

C) $6^x^{2} ^+^1\ \textless \ 6^5$

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\sf \left(\dfrac{1}{81}\right)^x \geq 9^{\:x + 3}$

$\sf \left(9^{-2}\right)^x \geq 9^{\:x + 3}$

$\sf \left9^{-2x} \geq 9^{\:x + 3}$

$\sf -2x \geq x + 3$

$\sf 2x \leq -x - 3$

$\sf 3x \leq - 3$

$\boxed{\boxed{\sf x \leq - 1}}$

$\sf (\sqrt{5})^x < 125$

$\sf 5^{\frac{x}{2}} < 5^3$

$\sf \dfrac{x}{2} < 3$

$\boxed{\boxed{\sf x < 6}}$

$\sf 6^{\:x^2 + 1} < 6^5$

$\sf x^2 + 1 < 5$

$\sf x^2 < 4$

$\sf -\sqrt{4} < x < \sqrt{4}$

$\boxed{\boxed{\sf -2 < x < 2}}$