CAT 2020

Slot 3

QA

Question & Solution

$\frac{2\times4\times8\times16}{(\log_{2}{4})^{2}(\log_{4}{8})^{3}(\log_{8}{16})^{4}}$

= $\frac{2^1\times2^2\times2^3\times2^4}{(\log_22^2)^2(\log_{2^2}2^3)^3(\log_{2^3}2^4)^4}$

= $\frac{2^{1+2+3+4}}{(2)^2(\frac{3}{2})^3(\frac{3}{2})^4}$

= $\frac{2^{10}}{4\left(\frac{3}{2}\right)^3\left(\frac{4}{3}\right)^4}=24$