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  4. Value of [( logb a)( logc b)( loga c)] is

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Q. Value of $\left[\left(\log_{b}\,a\right)\left(\log_{c}\,b\right)\left(\log_{a}\,c\right)\right]$ is

UPSEEUPSEE 2016

Solution:

$\left(\log _{b}\right.$ a) $\left(\log _{c} b\right)\left(\log _{a} c\right)$
$=\frac{\log a}{\log b} \times \frac{\log b}{\log c} \times \frac{\log c}{\log a}\left[\because \log _{m} n=\frac{\log n}{\log m}\right]$
$=1$