Question

Prove that:

${\log }_{b^3}a\times {\log }_{c^3}b\times {\log }_{a^3}c=\frac{1}{27}$.

Answer 1

Now,

${\log }_{b^3}a\times {\log }_{c^3}b\times {\log }_{a^3}c$

$=\frac{1}{3}{\log }_{b}a\times \frac{1}{3}\times {\log }_{c}b\times \frac{1}{3}\times {\log }_{a}c$

$=\frac{1}{27}\times \frac{\log a}{\log b}\times \frac{\log b}{\log c}\times \frac{\log c}{\log a}$

$=\frac{1}{27}$.