CAT 2020 Quant Question [Slot 3] with Solution 23

Question

\(\frac{{2 \times 4 \times 8 \times 16}}{{{{\left( {{{\log }_2}4} \right)}^2}{{\left( {{{\log }_4}8} \right)}^3}{{\left( {{{\log }_8}16} \right)}^4}}}\) equals

Option: 24
Solution:

\({\log _2}4 = 2;{\log _4}8 = \frac{3}{2};{\log _8}16 = \frac{4}{3}\)

\(\frac{{2 \times 4 \times 8 \times 16}}{{{{\left( {{{\log }_2}4} \right)}^2} \times {{\left( {{{\log }_4}8} \right)}^3} \times {{\left( {{{\log }_8}16} \right)}^4}}} = \frac{{2 \times 4 \times 8 \times 16}}{{{{(2)}^2} \times {{(3/2)}^3} \times {{(4/3)}^4}}} = 24\)

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CAT 2020 Quant questions with Solutions