Question

Resolva as inequações abaixo: a) 2^ x+7<32
b) 4< 2^x+1 ≤ 32
c) 3^x-2 > 9
d) (1/3)^x > 1/81
e) 2^ 5x > 2^3x+10

Answer 1

Explicação passo-a-passo:

a)

$\sf 2^{x+7} < 32$

$\sf 2^{x+7} < 2^5$

$\sf x+7 < 5$

$\sf x < 5-7$

$\sf x < -2$

b)

$\sf 4 < 2^{x+1}\le32$

$\sf 2^2 < 2^{x+1}\le2^5$

$\sf 2 < x+1\le5$

$\sf 2-1 < x\le5-1$

$\sf 1 < x\le4$

c)

$\sf 3^{x-2} > 9$

$\sf 3^{x-2} > 3^2$

$\sf x-2 > 2$

$\sf x > 2+2$

$\sf x > 4$

d)

$\sf \left(\dfrac{1}{3}\right)^x > \dfrac{1}{81}$

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

$\sf x < 4$

e)

$\sf 2^{5x} > 2^{3x+10}$

$\sf 5x>3x+10$

$\sf 5x-3x>10$

$\sf 2x>10$

$\sf x>\dfrac{10}{2}$

$\sf x>5$