Difference between revisions of "1983 AHSME Problems/Problem 12"
Sevenoptimus (talk | contribs) (Fixed problem statement and formatting, and made consequential corrections to the solution) |
Sevenoptimus (talk | contribs) m (Further fixed the solution) |
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==Solution== | ==Solution== | ||
− | Because <math>\log_7 \Big(\log_3 (\log_2 x) \Big) = 0</math>, we deduce <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>. Since <math>x=8</math>, <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== |
Revision as of 18:50, 26 January 2019
Problem 12
If , then
equals
Solution
Because , we deduce
, and thus
. Therefore,
. Since
,
. 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 |
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