Question

Log2 8/x - 10(log2 16x)>0

Answer 1

$log_{2} \frac{8}{x} -10 log_{2} (16x)\ \textgreater \ 0$
ОДЗ: 8/x>0
x>0
$log_{2} {8}- log_{2} {x} -10 (log_{2} 16+ log_{2} x)\ \textgreater \ 0$
$3- log_{2} {x} -40-10 log_{2} x\ \textgreater \ 0$
$-11 log_{2} x\ \textgreater \ 37$
$log_{2} x\ \textless \ - \frac{37}{11}$
$log_{2} x\ \textless \ log_{2} 2^{- \frac{37}{11} }$
$x\ \textless \ 2^{- \frac{37}{11} }$
Ответ: (0; $2^{- \frac{37}{11} }$)