Question

Resolva as equações exponenciais: a) (2^x)^x=16 b)(3^x)^x-4=1/27

Answer 1

a) (2^x)^x = 16
(2)^x.x = 2^4
x.x = 4
x^2 = 4
x = raíz quadr de 4
x = +/- 2

b) (3^x)^x-4 = 1/27
(3)^x.(x - 4) = 27^(- 1)
(3)^(x^2 - 4x) = ((3)^3)^(- 1)
(3)^(x^2 - 4x) = (3)^(- 3)
x^2 - 4x = - 3
x^2 - 4x + 3 = 0
Delta = b^2 - 4.a.c
Delta = (- 4)^2 - 4.1.3 = 16 - 12 = 4
x = (- b +/- raíz quadr de delta)/2.a
x1 = ( -(- 4) + raíz quadr de 4)/2.1
x1 = (4 + 2)/2 = 6/2 = 3
x2 = (4 - 2)/2 = 2/2 = 1
x1 = 3 e x2 = 1.