Difference between revisions of "2021 AMC 12B Problems/Problem 21"
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<math>\textbf{(A) }S<\sqrt2 \qquad \textbf{(B) }S=\sqrt2 \qquad \textbf{(C) }\sqrt2<S<2\qquad \textbf{(D) }2\le S<6 \qquad \textbf{(E) }S\ge 6</math> | <math>\textbf{(A) }S<\sqrt2 \qquad \textbf{(B) }S=\sqrt2 \qquad \textbf{(C) }\sqrt2<S<2\qquad \textbf{(D) }2\le S<6 \qquad \textbf{(E) }S\ge 6</math> | ||
| − | ==Solution== | + | == Video Solution by OmegaLearn (Logarithmic Tricks) == |
| − | + | https://youtu.be/uCTpLB-kGR4 | |
| + | |||
| + | ~ pi_is_3.14 | ||
==See Also== | ==See Also== | ||
{{AMC12 box|year=2021|ab=B|num-b=20|num-a=22}} | {{AMC12 box|year=2021|ab=B|num-b=20|num-a=22}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 21:47, 11 February 2021
Problem
Let 
be the sum of all positive real numbers 
for which![\[x^{2^{\sqrt2}}=\sqrt2^{2^x}.\]](http://latex.artofproblemsolving.com/9/1/d/91d43f026978eb57bfbe0d83263ca432924008bf.png)
Which of the following statements is true?
Video Solution by OmegaLearn (Logarithmic Tricks)
~ pi_is_3.14
See Also
| 2021 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 20 |
Followed by Problem 22 |
| 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 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
