$\log_a \dfrac{a}{b} + \log_a \dfrac{b}{c} + \log_a \dfrac{c}{a} = ?$ (telescoping)

Combining the logs gives $\log_a\!\left(\dfrac{a}{b}\cdot\dfrac{b}{c}\cdot\dfrac{c}{a}\right) = \log_a 1$. Since every factor cancels, the argument equals $1$, and $\log_a 1 = 0$ for any base.