Question

Решить неравенство:....

Answer 1

$log_\frac{1}{4}(x+7)-log_{\frac{1}{4}}4\ \textgreater \ 0\; ,\; ODZ:\; x\ \textgreater \ -7\\\\log_{\frac{1}{4}}\frac{x+7}{4}\ \textgreater \ 0\\\\\frac{x+7}{4}\ \textless \ 1\\\\\frac{x+7-4}{4}\ \textless \ 0\\\\x+3\ \textless \ 0\\\\x\ \textless \ -3\\\\Otvet:\; -7\ \textless \ x\ \textless \ -3$

Answer 2

Log₁/₄(x+7)-log₁/₄4>0
log₁/₄(x+7)>log₁/₄4

0<1/4<1  знак неравенства меняем
{x+7<4             {x<-3
 x+7>0              x>-7
               / / / / / / / / / / / / /  / /  / /
------------|--------------|------------>x
             -7               -3
  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
x∈(-7;-3)