cat 2020 Question 10

Question

$\frac{2 imes 4 imes 8 imes 16}{(\log_2{4})^{2} (\log_4{8})^3 (\log_8{16})^4}$ equals

Accepted Answer

$\frac{2×4×8×16}{(log_{2}4)^{2}(log_{4}8)^{3}(log_{8}16)^{4}}$

$\frac{2^1×2^2×2^3×2^4}{(log_{2}2^2)^{2}(log_{2^2}2^3)^{3}(log_{2^3}2^4)^{4}}$

$\frac{2^{1+2+3+4}}{(2^2)(\frac32)^{3}(\frac32)^{4}}$

$\frac{2^{10}}{4(\frac32)^{3}(\frac43)^{4}}$ = 24

Question 10.