1983 AHSME Problems/Problem 12

Problem 12

If $\log_7 \Big(\log_3 (\log_2 x) \Big) = 0$ , then $x^{-1/2}$ equals

$\textbf{(A)} \ \frac{1}{3} \qquad \textbf{(B)} \ \frac{1}{2 \sqrt 3} \qquad \textbf{(C)}\ \frac{1}{3\sqrt 3}\qquad \textbf{(D)}\ \frac{1}{\sqrt{42}}\qquad \textbf{(E)}\ \text{none of these}$

Solution

Because $\log_7 \Big(\log_3 (\log_2 x) \Big) = 0$ , we deduce $\log_3 (\log_2 x) =1$ , and thus $\log_2 x=3$ . Therefore, $x=8$ . Since $x=8$ , $x^{-1/2}=\frac{1}{2\sqrt{2}}$ . Since this does not match any of the answer choices, the answer is $\fbox{{\bf(E)} \text{none of these}}$

1983 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 11	Followed by Problem 13
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1983 AHSME Problems/Problem 12

Problem 12

Solution

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