Prove the following identities:

log_b a . log_c b . log_d c = log_d a

Given,

log_ba . log_cb . log_dc = log_da

Simplifying L.H.S. we get,

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

Hence, proved that log_b a . log_c b . log_d c = log_d a.