0\; ,\\\frac{1}{32x^2}+1>0\; ,\\\frac{1}{16x}+1>0\; ,\end{array}\right\; \; \left\{\begin{array}{ccc}x>-\frac{1}{2}\\\frac{32x^2+1}{32x^2}>0 \\\frac{16x+1}{16x}>0\end{array}\right\\\\\frac{32x^2+1}{32x^2}>0\; ,\; \; tak\; kak\; \; 32x^2+1>0\; pri\; x\in R\; \; \to \; \; x\ne 0\\\\\frac{16x+1}{16x}>0\; ,\; \; x_1=-\frac{1}{16}\; ,\; x_2=0\\\\znaki:\; \; \; +++(-\frac{1}{16})---(0)+++\\\\x\in (-\infty ,-\frac{1}{16})\cup (0,+\infty )" alt="log_3(2x+1)+log_3(\frac{1}{32x^2}+1)\geq log_3(\frac{1}{16x}+1)\\\\ODZ:\; \; \left\{\begin{array}{ccc}2x+1>0\; ,\\\frac{1}{32x^2}+1>0\; ,\\\frac{1}{16x}+1>0\; ,\end{array}\right\; \; \left\{\begin{array}{ccc}x>-\frac{1}{2}\\\frac{32x^2+1}{32x^2}>0 \\\frac{16x+1}{16x}>0\end{array}\right\\\\\frac{32x^2+1}{32x^2}>0\; ,\; \; tak\; kak\; \; 32x^2+1>0\; pri\; x\in R\; \; \to \; \; x\ne 0\\\\\frac{16x+1}{16x}>0\; ,\; \; x_1=-\frac{1}{16}\; ,\; x_2=0\\\\znaki:\; \; \; +++(-\frac{1}{16})---(0)+++\\\\x\in (-\infty ,-\frac{1}{16})\cup (0,+\infty )" align="absmiddle" class="latex-formula">
-\frac{1}{2}\qquad \qquad \qquad \qquad \\x\ne 0\qquad \qquad \qquad \qquad \\x\in (-\infty ,-\frac{1}{16})\cup (0,+\infty )\end{array}\right\; \; \; \Rightarrow \; \; x\in (-\frac{1}{2}\, ,\, -\frac{1}{16})\cup (0,+\infty )" alt="\left\{\begin{array}{ccc}x>-\frac{1}{2}\qquad \qquad \qquad \qquad \\x\ne 0\qquad \qquad \qquad \qquad \\x\in (-\infty ,-\frac{1}{16})\cup (0,+\infty )\end{array}\right\; \; \; \Rightarrow \; \; x\in (-\frac{1}{2}\, ,\, -\frac{1}{16})\cup (0,+\infty )" align="absmiddle" class="latex-formula">