CAT (QA) PYQs

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

The value of $\log_a \left(\frac{a}{b}\right) + \log_b \left(\frac{b}{a}\right)$, for $1 < a \leq b$ cannot be equal to

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