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  4. The value of ( log3 5 × log25 27 × log49 7/ log81 3) is

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Q. The value of $\frac{\log_{3} 5 \times \log_{25} 27 \times \log_{49} 7}{\log_{81} 3}$ is

WBJEEWBJEE 2010

Solution:

$\frac{\left(\frac{\log 5}{\log 3} \times \frac{3 \log 3}{2 \log 5} \times \frac{\log 7}{2 \log 7}\right)}{\left(\frac{\log 3}{4 \log 3}\right)} $
$=3\left[\because \log _{a} b=\frac{\log b}{\log a}\right]$