Question

Respondam por favor!​

Answer 1

Resposta:

letra a)

${8}^{x - 9} = {16}^{ \frac{x}{2} } \\ {2}^{3(x - 9)} = {2}^{4( \frac{x}{2}) } \\ 3x - 27 = \frac{4x}{2} \\ 3x - 27 = 2x \\ 3x - 2x = 27 \\ x = 27$

letra b)

${(0.1)}^{2 {x}^{2} - x - 1 } = 1 \\ {(0.1)}^{2 {x}^{2} - x - 1 } = (0.1) ^{0} \\ 2x^{2} - x - 1 = 0$

∆=(-1)²-4.2.-1 = 1+8 = 9

x'

$\frac{ - ( - 1) - \sqrt{9} }{2 \times 2} = \frac{1 - 3}{4} = \frac{ - 2}{4} = \frac{ - 1}{2}$

x"

$\frac{ - ( - 1) + \sqrt{9} }{2 \times 2} = \frac{1 + 3}{4} = \frac{ 4}{4} = 1$

letra c)

$4 \sqrt[4]{ {2}^{x} } = 16 \\ \sqrt[4]{ {2}^{x} } = \frac{16}{4} \\ \sqrt[4]{ {2}^{x} } = 4 \\ {2}^{ \frac{x}{4} } = {2}^{2} \\ \frac{x}{4} = 2 \\ x = 4 \times 2 \\ x = 8$