CAT (QA) PYQs

If $p^3 = q^4 = r^5 = s^6$, then the value of $\log_s(pqr)$ is equal to

$\small \dfrac{2\times4\times8\times16}{(\log_2 4)^2 (\log_4 8)^3 (\log_8 16)^4}$ is equal to

$\dfrac{1}{\log _{2} 100}-\dfrac{1}{\log _{4} 100}+\dfrac{1}{\log _{5} 100}-\dfrac{1}{\log _{10} 100}+\dfrac{1}{\log _{20} 100}-\dfrac{1}{\log _{25} 100}+\dfrac{1}{\log _{50} 100}= \ ?$