0\\\\2log_2x+2log_2x-log_2x=9\\\\3log_2x=9\\\\log_2x=3\\\\x=2^3=8" alt="1)\; 2log_2x+log_{\sqrt2}x+log_{\frac{1}{2}}x=9\; ,\; \; ODZ:\; x>0\\\\2log_2x+2log_2x-log_2x=9\\\\3log_2x=9\\\\log_2x=3\\\\x=2^3=8" align="absmiddle" class="latex-formula">
0} \atop {2x-3>0}} \right. \; ,\; \left \{ {{x>-6} \atop {x>\frac{3}{2}}} \right. \; \to \; x>\frac{3}{2}\\\\lg(x+6)-lg\sqrt{2x-3}=lg10^2-lg25\\\\lg(x+6)=lg\sqrt{2x-3}+lg\frac{100}{25}\\\\lg(x+6)=lg\sqrt{2x-3}+lg4\\\\x+6=4\sqrt{2x-3}\\\\16(2x-3)=x^2+12x+36\\\\x^2-20x+84=0\\\\x_1=6,\; x_2=14\; (teor.\; Vieta)\\\\Otvet:\; 6,\; 14." alt="2)lg(x+6)-\frac{1}{2}lg(2x-3)=2-lg25\; ,\\\\ODZ:\; \left \{ {{x+6>0} \atop {2x-3>0}} \right. \; ,\; \left \{ {{x>-6} \atop {x>\frac{3}{2}}} \right. \; \to \; x>\frac{3}{2}\\\\lg(x+6)-lg\sqrt{2x-3}=lg10^2-lg25\\\\lg(x+6)=lg\sqrt{2x-3}+lg\frac{100}{25}\\\\lg(x+6)=lg\sqrt{2x-3}+lg4\\\\x+6=4\sqrt{2x-3}\\\\16(2x-3)=x^2+12x+36\\\\x^2-20x+84=0\\\\x_1=6,\; x_2=14\; (teor.\; Vieta)\\\\Otvet:\; 6,\; 14." align="absmiddle" class="latex-formula">