Difference between revisions of "1983 AHSME Problems/Problem 12"
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==Problem 12== | ==Problem 12== | ||
| − | If <math>\ | + | If <math>\log_7 \Big(\log_3 (\log_2 x) \Big) = 0</math>, then <math>x^{-1/2}</math> equals |
| − | <math>\ | + | <math>\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}</math> |
==Solution== | ==Solution== | ||
| − | Because <math>\ | + | Because <math>\log_7 \Big(\log_3 (\log_2 x) \Big) = 0</math>, we deduce <math>\log_3 (\log_2 x) =1</math>, and thus <math>\log_2 x=3</math>. Therefore, <math>x=8</math>, which means <math>x^{-1/2}=\frac{1}{2\sqrt{2}}</math>. Since this does not match any of the answer choices, the answer is <math>\fbox{{\bf(E)} \text{none of these}}</math>. |
==See Also== | ==See Also== | ||
Latest revision as of 23:47, 19 February 2019
Problem 12
If 
, then 
equals
Solution
Because , we deduce 
, and thus 
. Therefore, 
, which means 
. Since this does not match any of the answer choices, the answer is 
.
See Also
| 1983 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
