Question

Ajudem rapidinho por favor!

Answer 1

a)

$2^{3.(x-9)} =2^{-1.(x+1)} \\ 2^{3x-27}=2^{-x-1} \\ 3x - 27 = -x -1 \\4x=26\\x=\frac{13}{2}$

b)

$100^{x}=0,0001\\ 10^{2x} = 10^{-4}\\ 2x = -4\\ x = -2$

c)

$2^{3.(x^{2}-x)}=2^{2.(x+1)} \\ 2^{3x^{2}-3x } =2^{2x+2} \\ 3x^{2}  - 3x=2x+2\\ 3x^{2} -5x-2=0$

Δ = b² - 4.a.c

Δ = (-5)² - 4 . 3 . -2

Δ = 25 - 4. 3 . -2

Δ = 49

x = (-b ± √Δ)/2a

x' = -(-5 + √49)/2.3     x'' = -(-5 - √49)/2.3

x' = 12 / 6     x'' = -2 / 6

x' = 2     x'' = - 1 / 3

e)

$3^{3(x^{2}+1) } =3^{2.5x} \\ 3x^{2} +3 = 10x\\ 3x^{2} -10x+3=0$

Δ = b² - 4.a.c

Δ = (-10)² - 4 . 3 . 3

Δ = 100 - 4. 3 . 3

Δ = 64

x = (-b ± √Δ)/2a

x' = -(-10 + √64)/2.3     x'' = -(-10 - √64)/2.3

x' = 18 / 6     x'' = 2 / 6

x' = 3     x'' = 1 / 3

g)

$2^{3x} =(\frac{1}{4})\\ 2^{3x} = 2^{-2} \\ 3x=-2\\ x = \frac{-2}{3}$

h)

$3^{2(2x+1)}=3^{-2x}  \\4x + 2 = -2x\\6x = -2\\x = -\frac{1}{3}$