Question

scrrooo podem me ajudar

Answer 1

Resposta:

Explicação passo-a-passo:

1)

(1/16)^(3x-2) = 2^(2x)

2^(-4)^(3x-2) = 2^(2x)

-4.(3x-2) = 2x

-12x+8= 2x

8 = 2x+12x

8= 14x (:2)

4= 7x

7x = 8

x= 8/7

______________

2)

(3/4)^(5x-5) > 1

(3/4)^(5x-5) > (3/4)^0

5x-5 > 0

5x > 5

x > 5/5

x > 1

R.: {x E R / x> 1}

______________

3)

81^x - 12.9^x + 27 = 0

[9^2]^x - 12.9^x + 27 = 0

(9^x)^2 - 12.9^x + 27 = 0

9^x = y

y^2 - 12y + 27 = 0

a = 1; b = -12; c = 27

∆= b^2 - 4ac

∆= 12^2 - 4.1.27

∆= 144-108

∆= 36

Y = [- b +/- √∆]/2a

Y = [-(-12) +/- √36]/2.1

Y = [12 +/- 6]/2

Y = [12+6]/2 = 18/2= 9

Y = [12-6]/2= 6/2= 3

9^x = y

9^x = 9^1

X= 1

9^x = y

9^x = 3

3^2x = 3^1

2x = 1

x = 1/2

81^x - 12.9^x + 27 = 0

=81^1 - 12.9^1 + 27

=81 - 12.9 + 27

= 81-108+27

= -27+27

= 0

81^x - 12.9^x + 27 = 0

= 81^1/2 - 12.9^(1/2) + 27

= √81 - 12.√9 + 27

= 9 - 12.3 + 27

= 9 - 36 + 27

= 36 - 36

= 0

R.:

x =1

x= 1/2