Question

Показательные неравенства. 50 БАЛЛОВ!
1) 37$37^{ frac{5x-9}{x+6} } leq 1$
2) $frac{29}{(30})^{ frac{9x-18}{x-6} }$>1

Answer 1

$37^{frac{5x-9}{x+6}} leq 1,; ; ; ; 37^{frac{5x-9}{x+6}} leq 37^0\\frac{5x-9}{x+6} leq 0,; ; ; x_1=frac{9}{5}=1,8,; x_2=-6\\+++(-6)---(frac{9}{5})+++\\xin (-6;frac{9}{5}]\\2); (frac{29}{30})^{frac{9x-18}{x-6}}>1,; ; 1=(frac{29}{30})^0\\frac{9x-18}{x-6}<0,; ; ; x_1=2,; x_2=6\\+++(2)---(6)+++\\xin (2;6)$