Question

Equacao exponencial 100¹-⁴x=0,0001?

Answer 1

$100^{1-4x}=0,0001$

$(10^2)^{1-4x}=\dfrac{1}{10000}$

$10^{2-8x}=10^{-4}$

Igualando os expoentes:

$2-8x=-4~\longrightarrow~-8x=-4-2~\longrightarrow~-8x=-6$

$x=\dfrac{-6}{-8}~\longrightarrow~x=\dfrac{6}{8}~\longrightarrow~\boxed{x=\dfrac{3}{4}}$

$\text{S}=\{\frac{3}{4}\}$