Question

Find out the value of
${\log }_{\sqrt{p}}\sqrt{q}\times {\log }_{\sqrt{q}}\sqrt{r}\times {\log }_{\sqrt{r}}\sqrt{p}$

Answer 1

$[Using{\log }_{a}b=\frac{\log b}{\log a}]$

$=\frac{\log \sqrt{q}}{\log \sqrt{p}}\times \frac{\log \sqrt{r}}{\log \sqrt{q}}\times \frac{\log \sqrt{p}}{\log \sqrt{r}}=1$