Question

resolva a equação 81 x+1=(1\3)x2 (2x)x=(1\4)x

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{81^{x + 1} = \left(\dfrac{1}{3}\right)^{x^2}}$

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

$\mathsf{3^{4x + 4} = 3^{-x^2}}$

$\mathsf{x^2 + 4x + 4 = 0}$

$\mathsf{(x + 2)^2 = 0}$

$\mathsf{x + 2 = 0}$

$\boxed{\boxed{\mathsf{x = -2}}}$

$\mathsf{(2^x)^x = \left(\dfrac{1}{4}\right)^{x}}$

$\mathsf{2x^2 = \dfrac{1}{4}}$

$\mathsf{x^2 = \dfrac{1}{8}}$

$\mathsf{x = \pm\: \dfrac{\sqrt{1}}{\sqrt{8}}}$

$\mathsf{x = \pm\: \dfrac{\sqrt{1}}{\sqrt{2^2.2}}}$

$\mathsf{x = \pm\: \dfrac{1}{2\sqrt{2}}}$

$\mathsf{x = \pm\: \dfrac{1}{2\sqrt{2}}\:.\:\dfrac{\sqrt{2}}{\sqrt{2}}}$

$\boxed{\boxed{\mathsf{x = \pm\: \dfrac{\sqrt{2}}{4}}}}$