Question

Решите неравенство 1/(5-log_2(4-2x)>0

Answer 1

$\displaystyle\cfrac{1}{5-\log_2(4-2x)}\ \textgreater \ 0;\left\{{{\log_2(4-2x)\neq5}\atop{\left\{{{5-\log_2(4-2x)\ \textgreater \ 0}\atop{4-2x\ \textgreater \ 0}}\right}}\right\to\left\{{{4-2x\neq32}\atop{\left\{{{\log_2(4-2x)\ \textless \ 5}\atop{x\ \textless \ 2}}\right}}\right\to\\\\\left\{{{x\neq-14}\atop{\left\{{{x\ \textgreater \ -14}\atop{x\ \textless \ 2}}\right}}\right~\to~x\in(-14;2)$

Answer 2

5- loq2(4-2X)>0
4-2X>0
Значить X неравен -14; Х>-14; и Х<2
X принадлежит (-12; 2)- решение неравенства