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

Question 1

Решите неравенство:
log(3)*(log1/3*x/1-x)<=3</span>

Question 2

$log_3(log_{\frac{1}{3}} \frac{x}{1-x}) \leq 3$ ;

1;" alt="3>1;" align="absmiddle" class="latex-formula">;
$0<log_{\frac{1}{3} \frac{x}{1-x} \leq 3^3$ ;
$0<log_{\frac{1}{3} \frac{x}{1-x} \leq 27$ ;
$0<\frac{1}{3}<1$ ;

\frac{x}{1-x} \geq (\frac{1}{3})^{27}" alt="(\frac{1}{3})^0>\frac{x}{1-x} \geq (\frac{1}{3})^{27}" align="absmiddle" class="latex-formula">;
$\frac{x}{1-x}=-\frac{-x}{1-x}=-\frac{1-x-1}{1-x}=\\\\-\frac{1-x}{1-x}+\frac{1}{1-x}=-1+\frac{1}{1-x}$ ;

\frac{1}{1-x} -1\geq 3^{-27}" alt="1>\frac{1}{1-x} -1\geq 3^{-27}" align="absmiddle" class="latex-formula">

\frac{1}{1-x} \geq 1+3^{-27}" alt="2>\frac{1}{1-x} \geq 1+3^{-27}" align="absmiddle" class="latex-formula">
$\frac{1}{2}<1-x \leq \frac{1}{1+3^{-27}}$
$-\frac{1}{2}<-x \leq -\frac{3^{-27}}{1+3^{-27}}$

x \geq \frac{1}{3^{27}+1}" alt="\frac{1}{2}>x \geq \frac{1}{3^{27}+1}" align="absmiddle" class="latex-formula">
x є $[\frac{1}{3^{27}+1};0.5)$

dtnth_zn · Answer 1 · 2018-03-15T00:06:36+0000