Question

(X-1)log_1/3(x) + 2log_1/3(x) > 0

Answer 1

$(x-1)log_{\frac{1}{3}}x+2log_{\frac{1}{3}}x>0\; \; ODZ:\; x>0,\\\\log_{\frac{1}{3}}x\cdot (x-1+2)>0\\\\1)\; \left \{ {{log_{\frac{1}{3}}x>0}} \atop {x+1>0}} \right. \; ,\; \left \{ {{0<x<1}} \atop {x>-1}} \right.\; \to \; 0<x<1}\\\\2)\left \{ {{log_{\frac{1}{3}}x<0}} \atop {x+1<0}} \right.\\\\\left \{ {{x>1}} \atop  {x<-1}} \right. \; \to \; sistema\; nesovmestna$