Question

Resolva as inequações exponenciais: (3/4)^x>3/4 (1/5)^x>1/25

Answer 1

Explicação passo-a-passo:

a)

$\sf \left(\dfrac{3}{4}\right)^x > \dfrac{3}{4}$

$\sf \left[\left(\dfrac{4}{3}\right)^{-1}\right]^x > \left(\dfrac{4}{3}\right)^{-1}$

$\sf \left(\dfrac{4}{3}\right)^{-x} > \left(\dfrac{4}{3}\right)^{-1}$

$\sf -x > -1$

$\sf -x > -1~~~\cdot(-1)$

$\sf x < 1$

$\sf \red{S=\{x\in\mathbb{R}~|~x < 1\}}$

b)

$\sf \left(\dfrac{1}{5}\right)^x > \dfrac{1}{25}$

$\sf (5^{-1})^x > 5^{-2}$

$\sf 5^{-x} > 5^{-2}$

$\sf -x > -2$

$\sf -x > -2~~~\cdot(-1)$

$\sf x < 2$

$\sf \red{S=\{x\in\mathbb{R}~|~x < 2\}}$