Question

Решить неравенство: 3log^21/3x-10log1/3x+3>0

Answer 1

$3log^{2} _{ \frac{1}{3} }x-10log_{ \frac{1}{3} }x+3 \geq 0 \\ log_{ \frac{1}{3} }x=t \\ 3t^2-10t+3 \geq 0 \\ D=100-4*3*3=64=8^2 \\ t_{1} = \frac{10+8}{6}=3 \\ \\ t_{2}= \frac{10-8}{6}= \frac{1}{3} \\ + - + \\ \left \{ {{log_{ \frac{1}{3} }x \leq 1/3} \atop {log_{ \frac{1}{3} }x \geq 3 }} \right. \left \{ {{x \leq \frac{1}{ \sqrt[3]3} } \atop {x \geq \frac{1}{9} }} \right. \\ x\ \textgreater \ 0\\ (0;\frac{1}{ \sqrt[3]3}] obedinenie promejytkov[ \frac{1}{9};+ \infty)$