[tex]5^{2*log_{5}(lg(x))}[/tex][tex]= lg(x) - lg^{2}(x) + 1[/tex]
[tex]2lg(x) = lg(x) - lg^{2}(x) + 1[/tex]
[tex]lg^{2}(x) = lg(x) - lg^{2}(x) + 1[/tex]
[tex]2 * lg^{2}(x) - lg(x) - 1 = 0[/tex]
[tex]notam\\lg(x) = t\\2t^{2} - t - 1 = 0\\t_1 = \frac{-1}{2} = > lg(x) = \frac{-1}{2} = > x = \frac{\sqrt{10} }{10}\\t_2 = 1 = > lg(x) = 1 = > x = 10\\S={10}[/tex]
