0} \atop {2x+3>0}} \right. \; \left \{ {{x\ne 0} \; \; \atop {x>-1,5}} \right\; \; \Rightarrow \; \; x\in (-1,5\, ;0)\cup (0;+\infty )\\\\\star \; \; a^{log_{b}c}=c^{log_{b}a}\; \; \star \\\\3^{2log_2|x|}+2\cdot 9^{log_2|x|}\leq 3\cdot 3^{-log_{0,5}(2x+3)}\\\\9^{log_2|x|}+2\cdot 9^{log_2|x|}\leq 3\cdot 3^{log_2(2x+3)}\\\\3\cdot 9^{log_2|x|}\leq 3\cdot 3^{log_2(2x+3)}\\\\3^{2log_2|x|}\leq 3^{log_2(2x+3)}" alt="3^{log_2x^2}+2\cdot |x|^{log_29}\leq 3\cdot \Big (\frac{1}{3}\Big )^{log_{0,5}(2x+3)}\\\\ODZ:\; \; \left \{ {{x^2>0} \atop {2x+3>0}} \right. \; \left \{ {{x\ne 0} \; \; \atop {x>-1,5}} \right\; \; \Rightarrow \; \; x\in (-1,5\, ;0)\cup (0;+\infty )\\\\\star \; \; a^{log_{b}c}=c^{log_{b}a}\; \; \star \\\\3^{2log_2|x|}+2\cdot 9^{log_2|x|}\leq 3\cdot 3^{-log_{0,5}(2x+3)}\\\\9^{log_2|x|}+2\cdot 9^{log_2|x|}\leq 3\cdot 3^{log_2(2x+3)}\\\\3\cdot 9^{log_2|x|}\leq 3\cdot 3^{log_2(2x+3)}\\\\3^{2log_2|x|}\leq 3^{log_2(2x+3)}" align="absmiddle" class="latex-formula">
![2log_2|x|\leq log_2(2x+3)\; \; ,\; \; |x|^2=x^2\; ,\\\\log_2x^2\leq log_2(2x+3)\\\\x^2\leq 2x+3\\\\x^2-2x-3\leq 0\; \; ,\; \; x_1=-1\; ,\; x_2=3\; \; (teorema\; Vieta)\\\\(x+1)(x-3)\leq 0\; \; \; +++[-1\, ]---[\, 3\, ]+++\\\\x\in [-1,3\, ]\\\\\left \{ {{x\in (-1,5\, ;\, 0)\cup (0\, ;+\infty )} \atop {x\in [-1,3\, ]}} \right. \; \; \Rightarrow \; \; \underline {\; x\in [-1,0)\cup (0,3\, ]\; }](https://tex.z-dn.net/?f=2log_2%7Cx%7C%5Cleq%20log_2%282x%2B3%29%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20%7Cx%7C%5E2%3Dx%5E2%5C%3B%20%2C%5C%5C%5C%5Clog_2x%5E2%5Cleq%20log_2%282x%2B3%29%5C%5C%5C%5Cx%5E2%5Cleq%202x%2B3%5C%5C%5C%5Cx%5E2-2x-3%5Cleq%200%5C%3B%20%5C%3B%20%2C%5C%3B%20%5C%3B%20x_1%3D-1%5C%3B%20%2C%5C%3B%20x_2%3D3%5C%3B%20%5C%3B%20%28teorema%5C%3B%20Vieta%29%5C%5C%5C%5C%28x%2B1%29%28x-3%29%5Cleq%200%5C%3B%20%5C%3B%20%5C%3B%20%2B%2B%2B%5B-1%5C%2C%20%5D---%5B%5C%2C%203%5C%2C%20%5D%2B%2B%2B%5C%5C%5C%5Cx%5Cin%20%5B-1%2C3%5C%2C%20%5D%5C%5C%5C%5C%5Cleft%20%5C%7B%20%7B%7Bx%5Cin%20%28-1%2C5%5C%2C%20%3B%5C%2C%200%29%5Ccup%20%280%5C%2C%20%3B%2B%5Cinfty%20%29%7D%20%5Catop%20%7Bx%5Cin%20%5B-1%2C3%5C%2C%20%5D%7D%7D%20%5Cright.%20%5C%3B%20%5C%3B%20%5CRightarrow%20%5C%3B%20%5C%3B%20%5Cunderline%20%7B%5C%3B%20x%5Cin%20%5B-1%2C0%29%5Ccup%20%280%2C3%5C%2C%20%5D%5C%3B%20%7D "2log_2|x|\leq log_2(2x+3)\; \; ,\; \; |x|^2=x^2\; ,\\\\log_2x^2\leq log_2(2x+3)\\\\x^2\leq 2x+3\\\\x^2-2x-3\leq 0\; \; ,\; \; x_1=-1\; ,\; x_2=3\; \; (teorema\; Vieta)\\\\(x+1)(x-3)\leq 0\; \; \; +++[-1\, ]---[\, 3\, ]+++\\\\x\in [-1,3\, ]\\\\\left \{ {{x\in (-1,5\, ;\, 0)\cup (0\, ;+\infty )} \atop {x\in [-1,3\, ]}} \right. \; \; \Rightarrow \; \; \underline {\; x\in [-1,0)\cup (0,3\, ]\; }")