Question

log1/3 log2(x^2)>0 пжлст

Answer 1

$log_{ \frac{1}{3}} log_2(x^2)\ \textgreater \ 0$
ОДЗ:
$\left \{ {{ x^{2} \ \textgreater \ 0} \atop {log_2x^2\ \textgreater \ 0}} \right.$
$\left \{ {{ x \neq 0} \atop {log_2x^2\ \textgreater \ log_21}} \right.$
$\left \{ {{ x \neq 0} \atop {x^2\ \textgreater \ 1}} \right.$
$\left \{ {{ x \neq 0} \atop {x^2-1\ \textgreater \ 0}} \right.$
$\left \{ {{ x \neq 0} \atop {(x-1)(x+1)\ \textgreater \ 0}} \right.$
$x$ ∈ $(-$ ∞ $;-1)$ ∪ $(1;+$ ∞ $)$

$log_{ \frac{1}{3}} log_2(x^2)\ \textgreater \ log_{ \frac{1}{3}} 1$
$log_2(x^2)\ \ \textless \ 1$
$log_2(x^2)\ \ \textless \ log_22$
$x^2\ \ \textless \ 2$
$x^2-2\ \textless \ 0$
$(x- \sqrt{2} )(x+ \sqrt{2} )\ \textless \ 0$

----+----(-√2)------_-------(√2)------+-------
                 /////////////////////
-----------------(-1)-----(1)--------------------
////////////////////              ///////////////////////

Ответ: $(- \sqrt{2} ;-1)$ ∪ $(1; \sqrt{2} )$