0} \atop {t \leq -\frac{2}{3}}} \right. " alt="1)\; \sqrt{log_{x}25+3}= \frac{1}{log_5x} \; ,\; ODZ:\; \left \{ {{x\ \textgreater \ 0,\; log_5x\ne 0} \atop {log_{x}25+3 \geq 0}} \right. \; , \left \{ {{x\ \textgreater \ 0\; ,\; x\ne 1} \atop {\frac{1}{log_{25}x}+3}\geq 0}} \right. \\\\\frac{1}{log_{25}x}+3=\frac{1}{\frac{1}{2}log_5x}+3=\frac{2}{log_5x}+3= \frac{2+3log_5x}{log_5x} \geq 0\; ,\\\\t=log_5x\; ,\; \frac{2+3t}{t} \geq 0\; ,\; \; \; +++(-\frac{2}{3})---(0)+++\; \; \left [ {{t > 0} \atop {t \leq -\frac{2}{3}}} \right. " align="absmiddle" class="latex-formula">
![x \leq 5^{-\frac{2}{3}}\; ,\; x \leq \frac{1}{\sqrt[3]{25}}\approx 0,34](https://tex.z-dn.net/?f=x+%5Cleq+5%5E%7B-%5Cfrac%7B2%7D%7B3%7D%7D%5C%3B+%2C%5C%3B+x+%5Cleq+%5Cfrac%7B1%7D%7B%5Csqrt%5B3%5D%7B25%7D%7D%5Capprox+0%2C34 "x \leq 5^{-\frac{2}{3}}\; ,\; x \leq \frac{1}{\sqrt[3]{25}}\approx 0,34")
0\; ,\; x > 1\\\\ODZ:\; \; x\in (0;\frac{1}{\sqrt[3]{25}}\, ]\cup (1,+\infty )\\\\log_{x}25+3=\frac{1}{log^2_5x}\; ,\; \; \frac{2}{log_5x}+3-\frac{1}{log^2_5x}=0\\\\ \frac{2log^2_5x+3log_5x-1}{log^2_5x}=0\; ,\; \; 2log^2_5x+3log_5x-1=0\; \Rightarrow \\\\log_5x=-1\; \; ili\; \; log_5x=\frac{1}{3}\\\\x=5^{-1}=\frac{1}{5}=0,2\; \; ili\; \; x=5^{\frac{1}{3}}=\sqrt[3]5\approx 1,71\\\\Otvet:\; \; 0,2\; \; ili\; \; \sqrt[3]5\; . " alt="log_5x > 0\; ,\; x > 1\\\\ODZ:\; \; x\in (0;\frac{1}{\sqrt[3]{25}}\, ]\cup (1,+\infty )\\\\log_{x}25+3=\frac{1}{log^2_5x}\; ,\; \; \frac{2}{log_5x}+3-\frac{1}{log^2_5x}=0\\\\ \frac{2log^2_5x+3log_5x-1}{log^2_5x}=0\; ,\; \; 2log^2_5x+3log_5x-1=0\; \Rightarrow \\\\log_5x=-1\; \; ili\; \; log_5x=\frac{1}{3}\\\\x=5^{-1}=\frac{1}{5}=0,2\; \; ili\; \; x=5^{\frac{1}{3}}=\sqrt[3]5\approx 1,71\\\\Otvet:\; \; 0,2\; \; ili\; \; \sqrt[3]5\; . " align="absmiddle" class="latex-formula">
![2)\; \sqrt{2log^2_2x+3log_2x-5}=log_2(2x)\; ,\; \; \; ODZ:\; \; \left \{ {{x\ \textgreater \ 0} \atop {2log^2_2x+3log_2x-5 \geq 0}} \right. \\\\2t^2+3t-5 \geq 0\; ;\; \; \; t_1=-2,5\; ,\; \; t_2=1\\\\+++(-2,5)---(1)+++\; \; \; \; \left [ {{t \geq 1} \atop {t \leq -2,5}} \right. \\\\log_2x \leq -2,5\; ;\; \; x \leq 2^{-2,5}\; ,\; \; x \leq \sqrt{2^{-5}}=\frac{1}{\sqrt{32}}\approx 0,18\\\\log_2x \geq 1\; ,\; \; x \geq 2\\\\ODZ:\; \; x\in (0;\sqrt{2^{-5}}\, ]\cup [2;+\infty )\\\\2log^2_2x+3log_2x-5=(1+log_2x)^2](https://tex.z-dn.net/?f=2%29%5C%3B+%5Csqrt%7B2log%5E2_2x%2B3log_2x-5%7D%3Dlog_2%282x%29%5C%3B+%2C%5C%3B+%5C%3B+%5C%3B+ODZ%3A%5C%3B+%5C%3B++%5Cleft+%5C%7B+%7B%7Bx%5C+%5Ctextgreater+%5C+0%7D+%5Catop+%7B2log%5E2_2x%2B3log_2x-5+%5Cgeq+0%7D%7D+%5Cright.+%5C%5C%5C%5C2t%5E2%2B3t-5+%5Cgeq+0%5C%3B+%3B%5C%3B+%5C%3B+%5C%3B+t_1%3D-2%2C5%5C%3B+%2C%5C%3B+%5C%3B+t_2%3D1%5C%5C%5C%5C%2B%2B%2B%28-2%2C5%29---%281%29%2B%2B%2B%5C%3B+%5C%3B+%5C%3B+%5C%3B++%5Cleft+%5B+%7B%7Bt+%5Cgeq+1%7D+%5Catop+%7Bt+%5Cleq+-2%2C5%7D%7D+%5Cright.+%5C%5C%5C%5Clog_2x+%5Cleq+-2%2C5%5C%3B+%3B%5C%3B+%5C%3B+x+%5Cleq+2%5E%7B-2%2C5%7D%5C%3B+%2C%5C%3B+%5C%3B+x+%5Cleq+%5Csqrt%7B2%5E%7B-5%7D%7D%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B32%7D%7D%5Capprox+0%2C18%5C%5C%5C%5Clog_2x+%5Cgeq+1%5C%3B+%2C%5C%3B+%5C%3B+x+%5Cgeq+2%5C%5C%5C%5CODZ%3A%5C%3B+%5C%3B+x%5Cin+%280%3B%5Csqrt%7B2%5E%7B-5%7D%7D%5C%2C+%5D%5Ccup+%5B2%3B%2B%5Cinfty+%29%5C%5C%5C%5C2log%5E2_2x%2B3log_2x-5%3D%281%2Blog_2x%29%5E2 "2)\; \sqrt{2log^2_2x+3log_2x-5}=log_2(2x)\; ,\; \; \; ODZ:\; \; \left \{ {{x\ \textgreater \ 0} \atop {2log^2_2x+3log_2x-5 \geq 0}} \right. \\\\2t^2+3t-5 \geq 0\; ;\; \; \; t_1=-2,5\; ,\; \; t_2=1\\\\+++(-2,5)---(1)+++\; \; \; \; \left [ {{t \geq 1} \atop {t \leq -2,5}} \right. \\\\log_2x \leq -2,5\; ;\; \; x \leq 2^{-2,5}\; ,\; \; x \leq \sqrt{2^{-5}}=\frac{1}{\sqrt{32}}\approx 0,18\\\\log_2x \geq 1\; ,\; \; x \geq 2\\\\ODZ:\; \; x\in (0;\sqrt{2^{-5}}\, ]\cup [2;+\infty )\\\\2log^2_2x+3log_2x-5=(1+log_2x)^2")
