![1)\; \; 2\, log_4\, 2^{4x}=2^{log_{\sqrt[3]2}2}\\\\2log_{2^2}\, 2^{4x}=2^{3log_22}\\\\log_2\, 2^{4x}=2^{log_28}\\\\4x=8\; ,\; \; \underline {x=2}](https://tex.z-dn.net/?f=1%29%5C%3B%20%5C%3B%202%5C%2C%20log_4%5C%2C%202%5E%7B4x%7D%3D2%5E%7Blog_%7B%5Csqrt%5B3%5D2%7D2%7D%5C%5C%5C%5C2log_%7B2%5E2%7D%5C%2C%202%5E%7B4x%7D%3D2%5E%7B3log_22%7D%5C%5C%5C%5Clog_2%5C%2C%202%5E%7B4x%7D%3D2%5E%7Blog_28%7D%5C%5C%5C%5C4x%3D8%5C%3B%20%2C%5C%3B%20%5C%3B%20%5Cunderline%20%7Bx%3D2%7D "1)\; \; 2\, log_4\, 2^{4x}=2^{log_{\sqrt[3]2}2}\\\\2log_{2^2}\, 2^{4x}=2^{3log_22}\\\\log_2\, 2^{4x}=2^{log_28}\\\\4x=8\; ,\; \; \underline {x=2}")
0} \atop {\frac{2}{x}>0}} \right. \; \left \{ {{x>-1} \atop {x>0}} \right.\; \to \; x>0\\\\\frac{x+1}{10}=\frac{2}{x}\; \; \to \; \; x^2+x=20\; ,\\\\x^2+x-20=0\; ,\; \; x_1=-5\; ,\; x_2=4>0\; \; (teorema\; Vieta)\\\\Otvet:\; \; x=4\; ." alt="2)\; \; log_5(\frac{x+1}{10})=log_5(\frac{2}{x})\; \; ,\; \; ODZ:\; \; \left \{ {{\frac{x+1}{10}>0} \atop {\frac{2}{x}>0}} \right. \; \left \{ {{x>-1} \atop {x>0}} \right.\; \to \; x>0\\\\\frac{x+1}{10}=\frac{2}{x}\; \; \to \; \; x^2+x=20\; ,\\\\x^2+x-20=0\; ,\; \; x_1=-5\; ,\; x_2=4>0\; \; (teorema\; Vieta)\\\\Otvet:\; \; x=4\; ." align="absmiddle" class="latex-formula">