Question

EQUAÇÃO EXPONENCIAL (determine o conjunto solução)

³√32^x ÷4^(x-1) = 8^(3x) ​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{\dfrac{(\sqrt[3]{\mathsf{32}})^x}{4^{x - 1}} = 8^{3x}}$

$\mathsf{\dfrac{(\sqrt[3]{\mathsf{2^5}})^x}{(2^2)^{x - 1}} = (2^3)^{3x}}$

$\mathsf{\dfrac{2^{5x/3}}{2^{2x - 2}} = 2^{9x}}$

$\mathsf{\dfrac{5x}{3} - (2x - 2) = 9x}$

$\mathsf{5x - 6x + 6 = 27x}$

$\mathsf{28x = 6}$

$\mathsf{x = \dfrac{6 \div 2}{28 \div2}}$

$\boxed{\boxed{\mathsf{x = \dfrac{3}{14}}}}$