log_9|x|\\\\\frac{lg|x|}{lg5}>\frac{lg|x|}{lg9}\\\\\frac{lg|x|}{lg5}-\frac{lg|x|}{lg9}>0\\\\\frac{lg|x|(lg9-lg5)}{lg9\cdot lg5}" alt="9^{log_{\frac{1}{9}}log_5x^2}<5^{log_{\frac{1}{5}}log_9x^2}\; ,\\\\9^{-log_9log_5x^2}<5^{-log_5log_9x^2}\\\\9^{log_9(log_5x^2)^{-1}}<5^{log_5(log_9x^2)^{-1}}\\\\\frac{1}{log_5x^2}<\frac{1}{log_9x^2}\\\\\frac{1}{2log_5|x|}<\frac{1}{2log_9|x|}\\\\log_5|x|>log_9|x|\\\\\frac{lg|x|}{lg5}>\frac{lg|x|}{lg9}\\\\\frac{lg|x|}{lg5}-\frac{lg|x|}{lg9}>0\\\\\frac{lg|x|(lg9-lg5)}{lg9\cdot lg5}" align="absmiddle" class="latex-formula">
Знаменатель дроби > 0, (lg9-lg5)>0, значит lg|x|>0
|x|>1 ---> x>1 или x<-1<br>Oтвет: хЄ(-беск, -1)U(1,+беск)