TMUA 2022 · Paper 1 · Question 20

Let $lo g_{b} x = y$ . Consider the following statements: I $lo g_{x} x^{y} = x$ II $lo g_{x} lo g_{y} y^{x} = x$ III $lo g_{y} lo g_{x} b = - 1$ Which of these statements is/are true for all permissible real numbers $x, y$ and $b$ ?