Question

AJUDA!!! Resolva, em IR, a inequação exponencial: (0,1)^3-4x menor ou igual a 0,001. Obs: ^ representa elevado

Answer 1

$\mathrm{(0,1)^{3-4x}\leq0,001\ \to\ \bigg(\dfrac{1}{10}\bigg)^{3-4x}\leq\bigg(\dfrac{1}{1000}\bigg)}\\\\ \mathrm{\big(10^{-1}\big)^{3-4x}\leq\bigg(\dfrac{1}{10^3}\bigg)\ \to\ 10^{4x-3}\leq10^{-3}}\\\\ \mathrm{*\ Comparando\ os\ expoentes:}\\\\ \mathrm{4x-3\leq-3\ \to\ 4x-3+3\leq-3+3}\\\\ \mathrm{4x\leq0\ \to\ \dfrac{4x}{4}\leq\dfrac{0}{4}\to\ \boxed{\mathbf{x\leq0}}}$

Answer 2

$( \frac{1}{10} )^{3-4x} \leq \frac{1}{1000} \\ \\ (10^{-1})^{3-4x} \leq 10^{-3} \\ \\ -3 + 4x \leq -3 \\ \\ 4x \leq -3 + 3 \\ \\ 4x \leq 0 \\ \\ x \leq 0$

Espero ter ajudado.