Question

As inequações que envolvem funções exponenciais são chamadas de inequações exponenciais. Das alternativas abaixo, qual representa o valor de x na inequação exponencial :
a.

x ≥ 1
b.

x ≥ –2
c.

x ≥ 2
d.

x ≤ –2
e.

x ≤ 2

Answer 1

$\left( \dfrac{5}{2}\right )^x \geq 0,16 \\\\\left( \dfrac{5}{2}\right )^x \geq \dfrac{16}{100} \\\\\left( \dfrac{5}{2}\right )^x \geq \dfrac{4}{25}\\\\\left( \dfrac{5}{2}\right )^x \geq \left(\dfrac{2^2}{5^2}\right)\\\\\left( \dfrac{5}{2}\right )^x \geq \left(\dfrac{2}{5}\right)^2\\\\\left( \dfrac{5}{2}\right )^x \geq \left(\dfrac{5}{2}\right)^{(-1) \cdot (2)}\\\\x \geq -2\\\\\boxed{\boxed{c) \ \geq -2}}$

Answer 2

Resposta:

$c)x \geqslant - 2$

Explicação passo-a-passo:

$( \frac{5}{2}) {}^{x} \geqslant 0.16$

$( \frac{5}{2} ) {}^{x} \geqslant \frac{16}{100}$

$( \frac{5}{2} ) {}^{x} \geqslant \frac{4}{25}$

$( \frac{5}{2} ) {}^{x} \geqslant ( \frac{2}{5} ) {}^{2}$

$( \frac{5}{2} ) {}^{x} \geqslant ( \frac{5}{2} ) {}^{ - 2}$

$x \geqslant - 2$