Difference between revisions of "2020 AMC 12A Problems/Problem 10"
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− | <cmath>\log_2{\frac{1}{4}\log_{2}{n}} = \frac{1}{2}\log_2({\frac{1}{2}\log_2{n}}).</cmath> | + | <cmath>\log_2({\frac{1}{4}\log_{2}{n}}) = \frac{1}{2}\log_2({\frac{1}{2}\log_2{n}}).</cmath> |
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+ | Using <math>\log</math> property of addition, we can expand the parentheses into | ||
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+ | <cmath>\log_2{(\frac{1}{4})}+\log_2{(\log_{2}{n}}) = \frac{1}{2}(\log_2{(\frac{1}{2})} +\log_{2}{(\log_2{n})}).</cmath> |
Revision as of 10:32, 1 February 2020
Solution
Any logarithm in the form .
so
becomes
Using property of addition, we can expand the parentheses into