0} \atop {x>0,\; x\ne 1}} \right. \; ,\; x\in (0,1)U(1,+\infty)\\\\log_5\sqrt{3x+4}\cdot \frac{1}{log_5x}=1\\\\log_5\sqrt{3x+4}=log_5x\\\\log_5\sqrt{3x+4}-log_5x=0\\\\log_5(\frac{\sqrt{3x+4}}{x})=log_51\\\\\frac{\sqrt{3x+4}}{x}=1\\\\\sqrt{3x+4}=x\\\\3x+4=x^2\\\\x^2-3x-4=0\\\\x_1=-1,\; x_2=4\in ODZ\\\\Otvet:\; x=4." alt="log_5\sqrt{3x+4}\cdot log_{x}5=1\; ,\\\\ODZ:\; \left \{ {{3x+4>0} \atop {x>0,\; x\ne 1}} \right. \; ,\; x\in (0,1)U(1,+\infty)\\\\log_5\sqrt{3x+4}\cdot \frac{1}{log_5x}=1\\\\log_5\sqrt{3x+4}=log_5x\\\\log_5\sqrt{3x+4}-log_5x=0\\\\log_5(\frac{\sqrt{3x+4}}{x})=log_51\\\\\frac{\sqrt{3x+4}}{x}=1\\\\\sqrt{3x+4}=x\\\\3x+4=x^2\\\\x^2-3x-4=0\\\\x_1=-1,\; x_2=4\in ODZ\\\\Otvet:\; x=4." align="absmiddle" class="latex-formula">