Question

СРОЧНО!!!
решите неравенство с помощью системы log₃ ( x +2)+ log₃x< log₃( 2x+ 1)

Answer 1

$log_3(x+2)+log_3x<log_3(2x+1)\\\\\\\left\{\begin{array}{l}x+2>0\\x>0\\2x+1>0\\x(x+2)<2x+1\end{array}\right\; \; \; \left\{\begin{array}{l}x>-2\\x>0\\x>-\frac{1}{2}\\x^2-1<0\end{array}\right\\\\\\\left\{\begin{array}{l}x>0\\(x-1)(x+1)<0\end{array}\right\; \; \; \left\{\begin{array}{l}x>0\\x\in (-1\, ;\, 1\; )\end{array}\right\; \; \; \Rightarrow \; \; \; \underline {\; x\in (\, 0\, ;\; 1\; )\; }\\\\\\Otvet:\; \; x\in (\; 0\; ;\; 1\; )\; .$

$\star \; \; \; (x-1)(x+1)<0\; \; ,\\\\znaki:\; \; +++(-1)---(1)+++\; \; ,\; \; \; \; \; x\in (-1\, ;\, 1\; )\; \; \; \star$