Question

Resolvendo em R a inequação log0,2(5x-1) < log 0,2 ^19 obtemos:

Answer 1

$\boxed{\begin{array}{l}\sf como~a~quest\tilde ao~n\tilde ao~est\acute a~muito~bem~escrita\\\sf vou~apresentar~duas~soluc_{\!\!,}\tilde oes. \\\sf 1^{\underline a}:~~\ell og_{0,2}5x-1<\ell og_{0,2}19\\\underline{\rm a~base~est\acute a~entre~0~e~1}\\\underline{\rm portanto~o~sentido~da~desigualdade~se~inverte.}\\\sf 5x-1>19\\\sf 5x>19+1\\\sf 5x>20\\\sf x>\dfrac{20}{5}\\\sf x>4\\\sf s=\{x\in\mathbb{R}/x>4\}\end{array}}$

$\boxed{\begin{array}{l}\sf 2^{\underline a}:~\ell og0,2\cdot(5x-1)<\ell og0,2^{19}\\\underline{\rm como~a~base~\acute e~maior~que~1~o~sentido~da~desigualdade~se~mant\acute em}.\\\sf x-0,2>0,2^{19}\\\sf x>0,2^{19}+0,2\\\sf x>0,2(0,2^{18}+1)\\\sf s=\{x\in\mathbb{R}/ x>0,2(0,2^{18}+1)\}\end{array}}$