Решите неравенство: [tex]log _{ \frac{2}{ \sqrt{5} } } \frac{5x}{5x-1} \ \textless \ 0[/tex]. Created by ashen. algebra-ru

ОДЗ:x∈(-∞;0)∪(1/5;+∞).Ответ: (1/5;+∞).

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August 2022 1 51 Report

Решите неравенство: [tex]log _{ \frac{2}{ \sqrt{5} } } \frac{5x}{5x-1} \ \textless \ 0[/tex]

Answers & Comments

zarembo73 $log_{ \frac{2}{ \sqrt{5} } } \frac{5x}{5x-1}\ \textless \ 0; \\ log_{ \frac{2}{ \sqrt{5} } } \frac{5x}{5x-1}\ \textless \ log_{ \frac{2}{ \sqrt{5} } }1; \\ \frac{5x}{5x-1}\ \textgreater \ 1; \\ \frac{5x-5x+1}{5x-1}\ \textgreater \ 0; \\ \frac{1}{5x-1}\ \textgreater \ 0; \\ 5x-1\ \textgreater \ 0; \\ 5x\ \textgreater \ 1; \\ x\ \textgreater \ \frac{1}{5}. \\$
ОДЗ:
$\frac{5x}{5x-1}\ \textgreater \ 0; \\ 5x(5x-1)\ \textgreater \ 0; \\$
x∈(-∞;0)∪(1/5;+∞).
Ответ: (1/5;+∞).

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