2022 AMC 10A Problems/Problem 11
Revision as of 22:53, 11 November 2022 by MRENTHUSIASM (talk | contribs) (Created page with "==Problem== Ted mistakenly wrote <math>2^m\cdot\sqrt{\frac{1}{4096}}</math> as <math>2\cdot\sqrt[m]{\frac{1}{4096}}.</math> What is the sum of all real numbers <math>m</math>...")
Problem
Ted mistakenly wrote as
What is the sum of all real numbers
for which these two expressions have the same value?
Solution
We are given that
Converting everything into powers of
we have
We multiply both sides by
, then rearrange and factor as
Therefore, we have
or
The sum of such values of
is
~MRENTHUSIASM
See Also
2022 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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 10 Problems and Solutions |
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