Question

Resolva, em R, as equações exponenciais (cálculo completo por favor):
a) 25x – 23.5X = 50
b) 100% – 1 = 9.(10x + 1)
C) 4x+1 – 33 • 2x + 8 = 0
d)9x-1-5.3x + 3x+1 = 27

Answer 1

Resposta:

a)

25^x - 23*5^x - 50 = 0

y^2 - 23y - 50 = 0

delta

d = 23^2 + 4*50 = 729

y1 = (23 + 27)/2 = 25 = 5^2

5^x = 5^2

x = 2

b)

100^x - 1 = 9*(10^x + 1)

y^2 - 1 = 9y + 9

y^2 - 9y - 10 = 0

y = 10

10^x = 10^1

x = 1

c)

y = 2^x

4y^2 - 33y + 8 = 0

delta

d = 33^2 - 4*4*8 = 961

y = (33 + 31)/8 = 8

y = (33 - 31)/8 = 1/4

2^x1 = 8 , x1 = 3

2^x2 = 1/4, x2 = -2

d)

9^(x - 1) - 5*3^x + 3^(x + 1) = 27

9^(x - 1) -5*3^x + 3*3^x = 27

9^(x - 1) - 2*3^x - 27 = 0

y = 3^x

y^2/9 - 2y - 27 = 0

y^2 - 18y - 243 = 0

delta

d = 324 + 4*243 = 1296

y = (18 + 36)/2 = 27

3^x = 27 = 3^3

x = 3