Question

решите неравенство:
log(3)*(log1/3*x/1-x)<=3

Answer 1

$log_3(log_{frac{1}{3}} frac{x}{1-x}) leq 3$;
$3>1;$;
$0<log_{frac{1}{3} frac{x}{1-x} leq 3^3$;
$0<log_{frac{1}{3} frac{x}{1-x} leq 27$;
$0<frac{1}{3}<1$;
$(frac{1}{3})^0>frac{x}{1-x} geq (frac{1}{3})^{27}$;
$frac{x}{1-x}=-frac{-x}{1-x}=-frac{1-x-1}{1-x}=\\-frac{1-x}{1-x}+frac{1}{1-x}=-1+frac{1}{1-x}$;
$1>frac{1}{1-x} -1geq 3^{-27}$
$2>frac{1}{1-x} geq 1+3^{-27}$
$frac{1}{2}<1-x leq frac{1}{1+3^{-27}}$
$-frac{1}{2}<-x leq -frac{3^{-27}}{1+3^{-27}}$
$frac{1}{2}>x geq frac{1}{3^{27}+1}$
x є $[frac{1}{3^{27}+1};0.5)$