Lg^2(5x+2)+lg(5x+2)^2=lg^2(50x+20) Верно ли тождество?
По правилам логарифмов lg (5x + 2)^2 = 2*lg (5x + 2) lg (50x + 20) = lg [10(5x + 2)] = lg 10 + lg (5x + 2) = 1 + lg (5x + 2) lg^2 (50x + 20) = [1 + lg (5x + 2)]^2 = 1 + 2*lg (5x + 2) + lg^2 (5x + 2) Получаем: левая часть lg^2 (5x + 2) + lg (5x + 2)^2 = lg^2 (5x + 2) + 2*lg (5x + 2) А правая часть lg^2 (50x + 20) = 1 + 2*lg (5x + 2) + lg^2 (5x + 2) Правая часть на 1 больше, чем левая.
![lg^2(50x+20) = [lg(10(5x+2))]^2 = [lg(5x+2)+lg10]^2 = \\ \\ = [lg(5x+2)+1]^2 = lg^2(5x+2)+2lg(5x+2)+1 = \\ \\ =lg^2(5x+2)+lg(5x+2)^2+1](https://tex.z-dn.net/?f=lg%5E2%2850x%2B20%29+%3D+%5Blg%2810%285x%2B2%29%29%5D%5E2+%3D+%5Blg%285x%2B2%29%2Blg10%5D%5E2+%3D++%5C%5C++%5C%5C+%3D++%5Blg%285x%2B2%29%2B1%5D%5E2+%3D+lg%5E2%285x%2B2%29%2B2lg%285x%2B2%29%2B1+%3D+%5C%5C++%5C%5C+%3Dlg%5E2%285x%2B2%29%2Blg%285x%2B2%29%5E2%2B1 "lg^2(50x+20) = [lg(10(5x+2))]^2 = [lg(5x+2)+lg10]^2 = \\ \\ = [lg(5x+2)+1]^2 = lg^2(5x+2)+2lg(5x+2)+1 = \\ \\ =lg^2(5x+2)+lg(5x+2)^2+1")