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Question 75
$$\frac{2\times4\times8\times16}{(\log_{2}{4})^{2}(\log_{4}{8})^{3}(\log_{8}{16})^{4}}$$ equals
Correct Answer: 24
Solution
$$\frac{2\times4\times8\times16}{(\log_{2}{4})^{2}(\log_{4}{8})^{3}(\log_{8}{16})^{4}}$$
= $$\frac{2^1\times2^2\times2^3\times2^4}{(\log_22^2)^2(\log_{2^2}2^3)^3(\log_{2^3}2^4)^4}$$
= $$\frac{2^{1+2+3+4}}{(2)^2(\frac{3}{2})^3(\frac{3}{2})^4}$$
= $$\frac{2^{10}}{4\left(\frac{3}{2}\right)^3\left(\frac{4}{3}\right)^4}=24$$
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