Logarithmic Value Range

Simplify the given expression: $\log_a \frac{a}{b} + \log_b \frac{b}{a} = (1 - \log_a b) + (1 - \log_b a) = 2 - \left(\log_a b + \log_b a\right)$ Let $t = \log_a b$. Since $1 < a \le b$, $t \ge 1$. By AM-GM, for $t \ge 1$, $t + \frac{1}{t} \ge 2$. Therefore: $2 - \left(t + \frac{1}{t}\right) \le 2 - 2 = 0$ So the value must be $\le 0$. Among the given options, $1 > 0$, so it cannot be equal to 1.