Evaluate :

log_b a × log_c b × log_a c

Simplifying the expression,

$\Rightarrow \text{log}$b a \times \text{log}c b \times \text{log}_a c \\[1em] \Rightarrow \dfrac{\text{log a}}{\text{log b}} \times \dfrac{\text{log b}}{\text{log c}} \times \dfrac{\text{log c}}{\text{log a}} \\[1em] \Rightarrow \dfrac{\text{log a.log b.log c}}{\text{log b.log c.log a}} \\[1em] \Rightarrow 1.

Hence, log_b a × log_c b × log_a c = 1.