Question

Resolva em R as inequações:

a) 16^(3x-1) > 8^(2x+5)

b) (0,3)^4x-5 > (0,3)^2x+1​

Answer 1

Resposta:

a)

${16}^{(3x - 1)} > {8}^{(2x - 5)}$

${2}^{4.(3x - 1)} > {2}^{3.(2x - 5)}$

${2}^{12x - 4} > {2}^{6x - 15}$

$12x - 4 > 6x - 15$

$6x > - 11$

$x > \frac{ - 11}{6}$

b)

${ \frac{3}{10} }^{4x - 5} > { \frac{3}{10} }^{2x + 1}$

Quando a base for menor que 1 a gente deve inverter a "boquinha"

$4x - 5 < 2x + 1$

$2x < 6$

$x < 3$