Question

Resolva a equação exponencial na incógnita x = (10x) elevado a 1 - x = 0,000001
alguém me ajuda? :)

Answer 1

$(10^x)^{1-x}=0,000001\\ 10^{x(1-x)}= \dfrac{1}{1000000}\\\\ 10^{-x^2+x}= \dfrac{1}{10^6}\\\\ \not10^{-x^2+x}=\not10^{-6}\\\\ -x^2+x=-6\\ x^2-x-6=0\\\\ x_1=-2~~e~~x_2=3\\\\\\ \Large\boxed{\text{S}=\{-2,~3\}}$