нужно перейти к одинаковому основанию
0, \ \ x\neq1\\ log_{0,5}x + \frac{3}{log_{0,5}x} =4\ \ \ \ \ \ |*log_{0,5}x\\ log^{2}_{0,5}x - 4log_{0,5}x +3 = 0\\ log_{0,5}x = t\\ t^{2} - 4t+3=0\\ t_{1}=1, \ t_{2}=3\\ log_{0,5}x = 1, \ \ \ \ log_{0,5}x = 3\\ x=0,5\ \ \ \ \ \ \ \ \ x=0,5^{3}\\ .\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=0,125 " alt="x>0, \ \ x\neq1\\ log_{0,5}x + \frac{3}{log_{0,5}x} =4\ \ \ \ \ \ |*log_{0,5}x\\ log^{2}_{0,5}x - 4log_{0,5}x +3 = 0\\ log_{0,5}x = t\\ t^{2} - 4t+3=0\\ t_{1}=1, \ t_{2}=3\\ log_{0,5}x = 1, \ \ \ \ log_{0,5}x = 3\\ x=0,5\ \ \ \ \ \ \ \ \ x=0,5^{3}\\ .\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=0,125 " align="absmiddle" class="latex-formula">