Question

докажите неравенство
(1/4) в 2+3x степени <8 в x-1 степени

Answer 1

$( \frac{1}{4})^{2+3x}\ \textless \ 8^{x-1}\\\\(2^{-2})^{2+3x}\ \textless \ (2^3)^{x-1}\\\\2^{-4-6x}\ \textless \ 2^{3x-3}\\\\2\ \textgreater \ 1\\\\-4-6x\ \textless \ 3x-3\\\\3x+6x\ \textgreater \ -4+3\\\\9x\ \textgreater \ -1\\\\x\ \textgreater \ - \frac{1}{9}\\\\x\in (- \frac{1}{9};+\infty)$