Question

equações exponenciais
a)11^2x^2-5x+2=1
b)9^x+1=∛3
c)0.2^x+1=√125
d) 0.25^x-4=0.5^-2x+1
e)(∛25)^x=(1/125)^-x+3

Answer 1

Ola Mellodoce

a)

11^(2x² - 5x + 2) = 1 = 11^0

2x² - 5x + 2 = 0

delta
d² = 25 - 16 = 9
d = 3

x1 = (5 + 3)/4 = 8(4 = 2
x2 = (5 - 3)/4 = 1/2

b)

9^(x + 1) = 3^(1/3)

3^(2x + 2) = 3^(1/3)

2x + 2 = 1/3
2x = 1/3 - 6/3 = -5/3
x = -5/6

c)

0.2 = 1/5

(1/5)^(x + 1) = 125^(1/2)

5^(-x-1) = 5^(3/2)

-x-1 = 3/2

x = -1 - 3/2 = -5/2

d)

0.25 = 1/4

(1/4)^(x - 4) = 1/2)^(-2x + 1)

(1/2)^(2x - 8) = 1/2(^(-2x + 1)

2x - 8 = -2x + 1
4x = 9

x = 9/4

e)

25^(x/3) = (1/125)^(-x+3)

5^(2x/3 = 5^(3x - 9)

2x/3 = 3x - 9

2x = 9x - 27

7x = 27
x = 27/7