Log4(5x+2)> log4(2x)

0 голосов
57 просмотров

Log4(5x+2)> log4(2x)


Математика (12 баллов) | 57 просмотров
0

5x+2>2x...

Дан 1 ответ
0 голосов

Переносим с правой в левую
image 0" alt=" log_{4}(5x + 2) - log_{4}(2x) > 0" align="absmiddle" class="latex-formula">
image 0" alt=" log_{4}( \frac{5x + 2}{2x} ) > 0" align="absmiddle" class="latex-formula">
image 4 ^{0} " alt=" \frac{5x + 2}{2x} > 4 ^{0} " align="absmiddle" class="latex-formula">
одз:
image 0" alt="5x + 2 > 0" align="absmiddle" class="latex-formula">
image - 2" alt="5x > - 2" align="absmiddle" class="latex-formula">
image - \frac{2}{5} " alt="x > - \frac{2}{5} " align="absmiddle" class="latex-formula">
image 0" alt="x > 0" align="absmiddle" class="latex-formula">
x \: ne \: ravno \: 0
общее одз х>0
image 2x" alt="5x + 2 > 2x" align="absmiddle" class="latex-formula">
image - 2" alt="5x - 2x> - 2" align="absmiddle" class="latex-formula">
image - 2" alt="3x > - 2" align="absmiddle" class="latex-formula">
image - \frac{2}{3} " alt="x > - \frac{2}{3} " align="absmiddle" class="latex-formula">
ответ:х>0

(3.6k баллов)