15. lg^2(x^3) / lg^3(x^2) * lg√x

lg^2(x^3) / lg^3(x^2) * lg√x = (lg(x^3))^2 / (lg(x^2))^3 * lg(x^(1/2)) = (3lgx)^2 / (2lgx)^3 * (1/2)lgx = 9(lgx)^2 / 8(lgx)^3 * (1/2)lgx = 9/8 * (1/2) = 9/16