# 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, $x=8$, which means $x^{-1/2}=\frac{1}{2\sqrt{2}}$. Since this does not match any of the answer choices, the answer is $\fbox{{\bf(E)} \text{none of these}}$.

## See Also

 1983 AHSME (Problems • Answer Key • Resources) Preceded byProblem 11 Followed byProblem 13 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 All AHSME Problems and Solutions

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