Question

Решите неравенство
$log_{2} (x-3) log_{2} (x-3)$<3

Answer 1

$log_2(x-3)log_2(x-3) textless 3; ,; ; ODZ:; ; x textgreater 3\\log^2_2(x-3)-3 textless 0\\(log_2(x-3)-sqrt3)(log_2(x-3)+sqrt3) textless 0\\t=log_2(x-3); ,; ; (t-sqrt3)(t+sqrt3) textless 0; to ; ; -sqrt3 textless t textless sqrt3\\ left { {{log_2(x-3) textgreater -sqrt3} atop {log_2(x-3) textless sqrt3}} right. ; left { {{x-3 textgreater 2^{-sqrt3}} atop {x-3 textless 2^sqrt3}} right. ; left { {{x textgreater 3+2^{-sqrt3}} atop {x textless 3+2^{sqrt3}}} right. \\Otvet:; ; xin (3+2^{-sqrt3};3+2^{sqrt3}).$