Difference between revisions of "2020 AMC 12A Problems/Problem 10"
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There is a unique positive integer <math>n</math> such that<cmath>\log_2{(\log_{16}{n})} = \log_4{(\log_4{n})}.</cmath>What is the sum of the digits of <math>n?</math> | There is a unique positive integer <math>n</math> such that<cmath>\log_2{(\log_{16}{n})} = \log_4{(\log_4{n})}.</cmath>What is the sum of the digits of <math>n?</math> | ||
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[[2020 AMC 12A Problems/Problem 10|Solution]] | [[2020 AMC 12A Problems/Problem 10|Solution]] | ||
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==Solution== | ==Solution== |
Revision as of 10:34, 1 February 2020
Problem
There is a unique positive integer such thatWhat is the sum of the digits of
Solution
Any logarithm in the form .
so
becomes
Using property of addition, we can expand the parentheses into